Questions on Algebra: Evaluation of expressions, parentheses answered by real tutors!

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(1/3)^2 + 1/4 - (4/3)^2 * (1/2)^3
-----
= (1/9) + (1/4) - (16/9)*(1/8)
= (13/36) - (8/36)
= 5/36
=============
Cheers,
Stan H.

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Evaluate {3(7 - 9) + 16}3 ÷ (-5) - 24
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= {3(-2) + 16}3 / (-5) - 24
= {-6+16}3 / (-5) -24
= {30}/(-5) -24
= -6 -24
= -30
==============
Cheers,
Stan H.

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Write 1024 in exponential notation
------
1024 = 2^10
===============
Cheers,
Stan H.

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Evaluate 2 * (5 - 3)^3 + 8 ÷ 2 + (9 - 4)^2
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= 2*2^3 + 4 + 5^2
= 2*8 + 4 + 25
= 45
=========
Cheers,
Stan H.

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A domain is a number or numbers that can be safely used in a function that do not create a zero.
SAMPLE:
What is the domain of y = 1/x?
The domain is:
ALL REAL NUMBERS except that x cannot = 0.
Because if x = 0, it creates division by zero, which does not exist.

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So

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3x^2-2x+1=0
.
Factoring the left side:
(3x+1)(x-1) = 0
.
Setting each term on the left to zero to find the set:
3x+1 = 0
3x = -1
x = -1/3
.
x-1 = 0
x = 1
.
Solution set:
x = {-1/3, 1}

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Could someone maybe tell me what I did wrong by these two problems;
(3a^2b)(-2ab^3)= 6a^3b4 (why is my answer wrong?)
----------------
You lost the minus sign. It's -6a^3b^4
-----------
or why is my answer wrong here; ab^2= 3(4)^2 = 3(4*4)=48
It would be more than great if someone could help me out here =)
--------------
I don't see a problem there.

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what I did wrong by these two problems;
(3a^2b)(-2ab^3)= 6a^3b4 (why is my answer wrong?)
or why is my answer wrong here; ab^2= 3(4)^2 = 3(4*4)=48
-------------------------
(3a^2b)(-2ab^3)= -6a^3b^4
----
It looks like you have substituted 3 for a and 4 for b.
If that is correct your answer is correct.
ab^2 = 3(4^2) = 3*16 = 48
===============================
Chers,
Stan H.

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Start with the given function


Plug in


Multiply


Subtract


Reduce

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, working eqn
Distribute:

Combine similar terms and perform operations:


, Answer
Subst. in working eqn to check:





Thank you,
Jojo

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==

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2x^2-3x+1=0
(2x-1)(x-1)=0
2x-1=0
2x=1
x=1/2 ans.
x-1=0
x=1 ans.

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=40-(18/-12)=41 1/2

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Which do you think?

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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 :
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18


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


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

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	18	1+18=19
2	9	2+9=11
3	6	3+6=9
-1	-18	-1+(-18)=-19
-2	-9	-2+(-9)=-11
-3	-6	-3+(-6)=-9

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.


So is prime.

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13(x+y)-11t(x+y)
Since both term has(x+y) as a common factor, pull it out:
(x+y)(13-11t)

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5x^2+5xy+19x+19y
Group:
(5x^2+5xy) + (19x+19y)
Factoring each group:
5x(x+y) + 19(x+y)
Factoring out (x+y):
(x+y)(5x+19)

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5x^2+5xy+19x+19y
5X(X+Y)+19(X+Y)
(5X+19)(X+Y) ans.

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(4a+5b)(b-a)

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x(5x-4)(3x-4)

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Factor:
This expression can be written as the difference of squares:

The difference of squares can be factored thus:
, so...

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Hi, Hope I can help,
.
factor -9b+63
.
First we need to find what is in common in both terms ( -9b and "63")
.
They both have a (-9) in common, now divide both terms by (-9)
.
=
.
=
.
Now we can combine the two answers, which equals , this makes up the second factor, first is (-9)
.
The factored form =
.
You would get the original polynomial if you used the distribution method
.
= = , remember the signs
.
, our original polynomial, they most likely want you to have "b" positive, so is your answer
.
Here is another way of factoring
.
They both have a "9" in common, now divide both terms by "9"
.
= =
.
=
.
Now we can combine the two answers, which equals , this makes up the second factor, first is "9"
.
The factored form = , we can check by distribution
.
= = (Remember signs)
.
, our original polynomial
.
They most likely want your "b" to be positive, so your factored answer is
.

.
Hope I helped, Levi

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factor out the negative of the greatest common factor: -9b+63
-------
= 9*(-b+7)
= -9*(b-7)
Either way.

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15x^3-32x^2+16x
x(15x^2-32x+16)
x(5x-4)(3x-4) ans.

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a^2-b^2+8a-8b
(a+b)(a-b)+8(a-b)
(8+a+b)(a-b) ans.

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16x^2-25y^2
(4x+5y)(4x-5y) ans.

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b^2-4b-5
(b-5)(b+1) ans.

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16x^2-40[x]+25 I'll assume you forgot the x.
(4x-5)(4x-5) or (4x-5)^2 ans.

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240=2x2x2x2x3x5
192=2x2x2x2x2x2x3
gcf=2x2x2x2x3=48 is the gcf.
Proof:
240/48=5
192/48=4

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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 the question is: what two whole numbers multiply to (the last term) and add to the second coefficient ?


To find these two numbers, we need to list all of the factors of .


Factors of :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30


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


These factors pair up and multiply to .
1*30
2*15
3*10
5*6
(-1)*(-30)
(-2)*(-15)
(-3)*(-10)
(-5)*(-6)

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	30	1+30=31
2	15	2+15=17
3	10	3+10=13
5	6	5+6=11
-1	-30	-1+(-30)=-31
-2	-15	-2+(-15)=-17
-3	-10	-3+(-10)=-13
-5	-6	-5+(-6)=-11

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 .


So the expression breaks down into

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25-3/7f=19+4/7f
-3f/7-4f/7=19-25
-7f/7=-6
-f=-6
f=6 ans.
25-3/7*6=19+4/7*6
25-18/7=19+24/7
25-19=24/7+18/7
6=42/7
6=6

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2ax-2bx+ay-by
I assume you want to factor.
When you have 4 terms, it is best to factor by groups.
2ax - 2bx = group 1
ay - by = group 2
======================================================
2ax - 2bx = 2x( a - b)
======================================================
ay - by = y(a - b)
Do you see the quantity (a - b)?
We only need one of them.
Final answer: (2x + y)(a - b)

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= when x = 3
It follows:



Thank you,
Jojo

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:
Recognize the numerator can be factored as the "difference of cubes"

:
Factor out -1 in the denominator and you have;

:
Cancel out the (x-1)'s and you have:

:
Which is:

;
Was this the "Major help" you needed?

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Start with the left side of the given equation.


Take half of the coefficient to get . In other words, .


Now square to get . In other words,


Now add and subtract . Make sure to place this after the "x" term. Notice how . So the expression is not changed.


Group the first three terms.


Factor to get .


Combine like terms.


So after completing the square, transforms to . So .


So is equivalent to .



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




Start with the given equation.


Add to both sides.


Combine like terms.


Take the square root of both sides.


or Break up the "plus/minus" to form two equations.


or Subtract from both sides.


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


Answer:


So the solutions are or .

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2x2 = 40
If you mean 2x^2=40 then:
x^2=40/2
x^2=20
x=sqrt20
x=2sqrt5 or 4.4721359 answer.

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Note: and where (in both cases)

So




So where

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So


Notes:

1) (otherwise a division by zero would occur)


2)


3)


3) Since , this means that

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simplify
(5x+1)^2(4x-4)^2
---------------
= 4*((5x+1)*(x-1))^2
That's as simplified as it gets. "simplify" needs to be defined.
If you meant to expand it:
=
=

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let the angles of the triangle be k, m, and r.
let k = 2*m
let k = c-r
-----
if k = 2*m, then m = k/2
-----
if k = r-5, then r = k+5
-----
since the sum of the interior angles of a triangle = 180 degrees, then
k + m + r = 180
substituting k/2 for m, and k+5 for r, we get:
k + k/2 + k + 5 = 180
-----
combining like terms, we get:
2*k + k/2 + 5 = 180
subtracting 5 from both side of the equation we get:
2*k + k/2 = 175
-----
since 2*k is the same as 4*k/2, we can substitute to get:
4*k/2 + k/2 = 175
since the denominators on the left hand side of the equation are the same, this equation becomes:
(4*k + k)/2 = 175
which becomes:
(5*k)/2 = 175
-----
multiplying both sides of the equation by 2 gets:
5*k = 350
dividing both sides of the equation by 5 gets:
k = 70
-----
k = 70
m = k/2 = 35
r = k+5 = 75
-----
70 + 35 + 75 = 180
-----
algebraic expression to solve the problem was derived above.
it started off as
k+m+r = 180
we solved for m in terms of k.
we solved for r in terms of k.
equation became:
k + (k/2) + (k+5) = 180
-----
the rest was simplification to come up with k = 70.
-----

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let the angles of the triangle be a, b, and c.
let a = 2*b
let a = c-5
-----
if a = 2*b, then b = a/2
-----
if a = c-5, then c = a+5
-----
since the sum of the interior angles of a triangle = 180 degrees, then
a + b + c = 180
substituting a/2 for b, and a+5 for c, we get:
a + a/2 + a + 5 = 180
-----
combining like terms, we get:
2*a + a/2 + 5 = 180
subtracting 5 from both side of the equation we get:
2*a + a/2 = 175
-----
since 2*a is the same as 4*a/2, we can substitute to get:
4*a/2 + a/2 = 175
since the denominators on the left hand side of the equation are the same, this equation becomes:
(4*a + a)/2 = 175
which becomes:
(5*a)/2 = 175
-----
multiplying both sides of the equation by 2 gets:
5*a = 350
dividing both sides of the equation by 5 gets:
a = 70
-----
a = 70
b = a/2 = 35
c = a+5 = 75
-----
70 + 35 + 75 = 180
-----
algebraic expression to solve the problem was derived above.
it started off as
a+b+c = 180
we solved for b in terms of a.
we solved for c in terms of a.
equation became:
a + (a/2) + (a+5) = 180
-----
the rest was simplification to come up with a = 70.
-----

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A binomial expression is simply an expression that is the sum (ie result of addition) of TWO monomials.


Now what is a monomial? A monomial is simply an expression that is the product of number (a coefficient) and variable term(s) (either one or more variable terms).

So for instance, we could have a coefficient of 2 and a variable term of "x", and the monomial would be 2*x or just 2x. Another example might have a coefficient of 10 and have the variable terms (you can have exponents) to get the monomial


Now using the two previous monomials, the binomial expression is


Another binomial expression is and another is .

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3x^2 + 2x – 8
(3x-4)(x+2)

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I am trying to find the gcf of x^2y, xy^2.
The GCF is the largest number that divides two or more numbers evenly.
The GCF in this case would be xy.