Questions on Algebra: Distributive, associative, commutative properties, FOIL answered by real tutors!

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Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:.


Multiply the Outer terms:.


Multiply the Inner terms:.


Multiply the Last terms:.


---------------------------------------------------


Now collect every term to make a single expression.


Now combine like terms.


So FOILs to .


In other words, .

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Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:.


Multiply the Outer terms:.


Multiply the Inner terms:.


Multiply the Last terms:.


---------------------------------------------------


Now collect every term to make a single expression.


Now combine like terms.


So FOILs to .


In other words, .

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Take note that




Start with the given expression.


Rewrite as . Rewrite as .


Now factor by using the sum of cubes formula. Remember the sum of cubes formula is


Multiply

-----------------------------------
Answer:

So factors to .


In other words,

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1. 2y + 3 -1/3(6x + 9y) + x
I simplified this way: 1/3(6x)=2x 1/3(9y)= 3y then 2y +3 -2x +3y +x= 2y+3y-2x+x+3= 5y+3x+3
------------------
2y + 3 -1/3(6x + 9y) + x
= 2y + 3 -2x -3y +x
= 3 -y -x
You had +3y, you overlooked the minus sign
----------------------------
2. 5x + 0(x +y) -3y +14 -3(y -x)
I simpified this way: 0(x)=x 0(y)=y 3(y)=3y 3(x)=3x then 5x+x+y-3y+14-3y-3x= 5x+1x-3x+1y-3y+14=3x-2y+14
----------------------
5x + 0(x +y) -3y +14 -3(y -x)
= 5x -3y +14 -3y +3x
= 8x -6y +14
You added an x and a y, even tho they're multiplied by zero. And, -3*-x = +3x
These things are tedious and error prone.

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1. the negative sign on the fraction (-1/3) distributes to the 3y
__ 2y + 3 - 2x - 3y + x = 3 - y - x


2. zero multiplied by ANY quantity is zero __ -3 times -x is 3x
__ 5x + 0 - 3y + 14 - 3y + 3x = 8x - 6y + 14

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Simplify:
1) =
2) =
Remember that zero times anything is always zero, so: 0(x+y) = 0

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Start with the given expression


Rewrite as


Rewrite as


Notice we have a difference of squares . In this case, and


So to factor this difference of squares, we can use the formula


So this means that


So factors to

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Start with the given expression.


Factor to get .


Factor to get .


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


Simplify.


Condense the expression


So simplifies to .


In other words, where or

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Start with the given expression.


Factor to get .


Factor to get .


Highlight the common terms.


Cancel out the common terms.


Simplify.


So simplifies to .


In other words, where or

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Start with the given expression


Multiply EVERY term by the inner LCD x to clear the inner denominators


Multiply and simplify


So simplifies to

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128r^2+448r+392
8(16x^2+56x+49)
8(4x+7)(4x+7) ans.

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your equation:
3x-(4+2x)
remove the parentheses:
3x - 4 - 2x
combine like terms:
x - 4
your new expression that is equivalent to your original expression:
x-4 = 3x-(4+2x)
-----
to prove, let x = 0:
0-4 = 0 - (4+0)
0-4 = 0-4
-4 = -4
-----
let x = 100:
100 - 4 = 3*100 - (4 + 2*100)
96 = 300 - (204)
96 = 96
-----
equations are equivalent.

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100 m/s (1/.3048 ft/m)= 328 ft/s (1/5280 mi/ft)=.062 mi/s (60 s/min)=
:
3.72 mi/min (60 min/hr)= mi/hr

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factor the right side
(2x+a)(x-b)=(2x-3)(x+2) or
.....................=(2x-2)(x+3/2)
so a and b are -3 and -2
...a and b are -2 and -3/2

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divide both sides by x+3

:
x=ax+b
:
in this format you can see that and

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1 square yard = 9 sq ft
so 100(9)=900 sq ft
:
.3048m=1ft
so .0929m^2=1sq ft
:
equals yd^2

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Area:


So


Find the area when x=3




This means that

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Start with the given expression.


Rewrite as . Rewrite as .


Now factor by using the difference of cubes formula. Remember the difference of cubes formula is


Multiply


Factor to get (by use of the difference of squares)


Factor to get

-----------------------------------
Answer:

So completely factors to .

In other words,

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Start with the given expression


Factor out the GCF


Now let's focus on the inner expression


------------------------------------------------------------

Start with the inner expression.


Rewrite as . Rewrite as .


Now factor by using the difference of cubes formula. Remember the difference of cubes formula is


Multiply


So factors to .

------------------------------------------------------------



Answer:
So completely factors to

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how would you solve square root -361/9
:

:
Both numerator and denominator are perfect squares, so think of it as:

We can use i which is sqrt(-1) so we have:
i

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Hi, Hope I can help,
.
If you are wanting us to solve this quadratic equation, here is how you do it.
.

.
The easiest way you can solve this is by factoring, in this case we can
.
First we need to write the "y"'s in parentheses
.
It is only "y" squared so there will be two "y"'s
.
( y )(y )
.
Next, we need to find the rest of the factors of this quadratic
.
If the factors of the third term, in this case "9", add up to the middle term( in this case (-6)), it can be factored
.
factors of "9" added together
.
(9) + (1) = 10
.
(-9) + (-1) = (-10)
.
(3) + (3) = 6
.
(-3) + (-3) = (-6)
.
The last pair of factors add up to the middle term
.
Now we will put the factors in the parentheses with the "y"'s
.
( y )(y ) = (y - 3 )(y - 3 )
.
This is the factored quadratic
.
( y - 3 )(y - 3 ) = 0, you can check by using the FOIL method ( First, Inner, Outer, Last )
.
= (F) = (O) = (I) = (L) , Remember the negative signs on the "3's"
.
, combine the like terms, (forget about the multiplication sign, it is just being weird) = ( True )
.
now we take each of the factors and have them equal "0", then solve for "y"
.
First factor = ( y - 3 )
.
, removing the parentheses
.
, moving (-3) to the right side
.
=
.
, the other factor is the same, so we would get the same answer.
.
your answer is , you can check by replacing "y" with "3" in the original equation
.
= = = = ( True )
.
You can also use the quadratic formula, for every quadratic equation, make sure your equation is in the form ( in this case "y" ) it is
.

.
a = 1
.
b = -6
.
c = 9
.
= = = = = =
.
Your answer is
.
Hope I helped, Levi

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lets call x the hypothenuse and sides a, a+1(because one side is one unit longer)
:
we know that but we also know that P=a+a+1+x::: 12=2a+1+x
:
x=11-2a----. plug this value into the 1st equation.
:
solve for a

:
divide by 2
:
factor
:

:

x=11-2a....11-2(20)=-29 so throw that out as its a negative length
...........11-2(3)=5
so one side is 3 the other side is 4 and the hypothenuse is 5

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Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .


Now multiply the first coefficient by the last term to get .


Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?


To find these two numbers, we need to list all of the factors of (the previous product).


Factors of :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to .
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

From the table, we can see that the two numbers and add to (the middle coefficient).


So the two numbers and both multiply to and add to


Now replace the middle term with . Remember, and add to . So this shows us that .


Replace the second term with .


Group the terms into two pairs.


Factor out the GCF from the first group.


Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


Combine like terms. Or factor out the common term

---------------------------------------------


Answer:


So factors to .


Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

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Need help with factoring
y^2-6y+9
-------------
You need to try it. Getting the answer isn't the same as knowing how to do it.

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Need help with factoring
x^2-36
i got
(x+6)(x-6)
Is this right?
-----------
Yes, it's right.
You can check my multiplying it out.

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x^4 - 13x^2 + 36
Factor this like an ordinary quadratic except you have:
:
(x^2 - 9)(x^2 - 4); (If you FOIL this you will get the original expression)
:
Note that each factor is the "difference of squares" and can be further factored
(x^2 - 9) = (x - 3)(x + 3)
and
(x^2 - 4) = (x - 2)(x + 2)

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Factor....Need some help
x^4-13x^2+36
----------------
It will be (x^2 + ?)*(x^2 + ?)
The ?'s product will be 36, and they add up to -13.
Since it's +36, they have to have the same sign, both Pos or both Neg.
Since they add to -13, they'll have to be both negative.
Consider the factors of 36:
1*36
2*18
3*12
4*9, and
6*6
They're the same sign, so that add to 13. If the were not the same sign, you would look at the differences.
Only 4 and 9 add to 13, so they're it.
It's (x^2 - 4)*(x^2 - 9)

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Looking at we can see that the first term is and the last term is where the coefficients are 1 and 36 respectively.

Now multiply the first coefficient 1 and the last coefficient 36 to get 36. Now what two numbers multiply to 36 and add to the middle coefficient -13? Let's list all of the factors of 36:



Factors of 36:
1,2,3,4,6,9,12,18

-1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 36
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13

First Number	Second Number	Sum
1	36	1+36=37
2	18	2+18=20
3	12	3+12=15
4	9	4+9=13
6	6	6+6=12
-1	-36	-1+(-36)=-37
-2	-18	-2+(-18)=-20
-3	-12	-3+(-12)=-15
-4	-9	-4+(-9)=-13
-6	-6	-6+(-6)=-12

From this list we can see that -4 and -9 add up to -13 and multiply to 36


Now looking at the expression , replace with (notice adds up to . So it is equivalent to )




Now let's factor by grouping:


Group like terms


Factor out the GCF of out of the first group. Factor out the GCF of out of the second group


Since we have a common term of , we can combine like terms

So factors to


So this also means that factors to (since is equivalent to )



So factors to

-----------------------------


Start with the given factorization


Factor to get (by use of the difference of squares)


Factor to get (by use of the difference of squares)



------------------------------------------------------------


Answer:


So completely factors to


Note: the order of the factors does not matter.

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Close, but the actual factorization is

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(1) -13=2b-b-10...Solve for b.
-13 = 2b - b - 10
-13 = b - 10
-13 + 10 = b
-3 = b
===============================
(2) 13=5-13+3a...Solve for a.
13 = 5 - 13 + 3a
13 = -8 + 3a
13 + 8 = 3a
21 = 3a
21/3 = a
7 = a
I hope this helps.

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Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:.


Multiply the Outer terms:.


Multiply the Inner terms:.


Multiply the Last terms:.


---------------------------------------------------


Now collect every term to make a single expression.


Now combine like terms.


So FOILs to .


In other words, .

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IF YOU JUST WANT TO COMBINE THESE TERMS THEN:
(5x^2–3x+2)+(-3x^2+9x–8)–(x^2+3x–10)
5X^2-3X+2-3X^2+9X-8-X^2-3X+10
X^2+3X+4 ans.

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6*(n+5) = (6*n) + (6*5) = 6n + 30
-2*(k+8) = (-2*k) + (-2*8) = -2k - 16
these are equivalent expressions that are equal to each other.
the distributive property states:
a*(b+c) = (a*b) + (a*c) = ab + ac
-----
the common multiplier (a) multiplies each term within the parentheses (b+c)
-----
the complicating factor is the signs of the operands.
you just have to remember:
minus times a minus makes a plus.
minus times a plus makes a minus.
-----
any number of operands can exist within the parentheses.
example:
a*(b+c+d+e) = (a*b) + (a*c) + (a*d) + (a*e)
-----

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9 a^2- 64 b^2
= (3a)^2- (8b)^2
= (3a+8b)(3a-8b)

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A five digit number is represented by ABCDE where each letter represents a digit.
:
If we add the digit 1 in front of ABCDE, we get 1ABCDE. The product of 1ABCDE
and 3 is the six digit number ABCDE1.
:
Find the value of the original number ABCDE
:
Starting from the right, side we know that E=7 because it's the only number
multiplied by 3 that will give last number as 1
:
We have:
1ABCD7
X 3
------
ABCD71; changed E to 7 here too
:
D = 5, multiplied 3, carry 2 to give us 17
we have
1ABC57
X 3
-------
ABC571; change D to 5 here too
:
C = 8, Multiplied by 3, carry 1 to give us 25
we have:
1AB857
X 3
--------
AB8571; change C to 8
:
B = 2, Multiplied by 3, carry 2, to give us 8
we have:
1A2857
X 3
-------
A28571; change B to 2
:
A = 4, multiplied by 3 gives 12
we have
142857
X 3
-----------
428571
:
ABCDE = 42857

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(3-b)6 =
This is not the Pythagorean Theorem.
This is called the distributive rule.
We multiply every term inside the parentheses by the outside number or term.
3 times 6 = 18
-b times 6 = -6b
Put it all together and we get:
18 - 6b.

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a^3+2abc-2c^2
a=3, b=9, and c=-2
3^3+2*3*9*-2-2(-2)^2
27-108-2*4
-81-8
-89 answer.

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Use the FOIL method:First*First+Outer*Outer+Inner*Inner+Last*Last
in this case x is the first term of the first binomial and 5x is the first term in the second binomial.
(x*5x)
+
x is the outermost term in the first binomial and (-9y) is the outermost term in the second binomial
(x*-9y)
+
(-4y) is the innermost term in the first binomial and 5x is the innermost term of the second binomial. So,
(-4y*5x)
+
-4y is the last term in the first binomial and -9y is the last term in the second binomial. So,
(-4y*-9y)
.

or

combine like terms and you get your final answer:
.
If you would like more consistency from tutoring, then consider making me your private tutor. For more information click on my name to go to my website or contact me at justin.sheppard.tech@hotmail.com

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So

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Name the Property.
a: 6+1*2=1*2+6
Ans: commutative
-----------------------
b: (7x)*y=7(xy)
Ans: associative
-----------------------
c: 0+a=a
Ans: additive identity
------------------------
d: 2(x+3)=2x+2*3
Ans: distributive
------------------------
e: 1/2(8*5)=(1/2*8)*5
Ans: associative
-----------------------
f: 1*(-2/3)=-2/3
Ans: multiplicative identity
==================================
Cheers,
Stan H.

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x2 – 15wy + 3xy – 5wx=
(-15wy-5wx=-5w(x+3y), so:
x2-5w(x+3y)+3xy=
(x2+3xy=x(x+3y), so:
x(x+3y)-5w(x+3y)=
(next factor out x+3y, so we have:
(x+3y)(x-5w)-----------------ans
CK using FOIL (First, Outer, Inner, Last)
x2-5wx+3xy-15wy or
x2-15wy+3xy-5wx
Hope this helps---ptaylor

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2x^3–26x^2+80x
2x(x^2-13x+40)
2x(x-8)(x-5)