SOLUTION: Someone should sue al-khwarizmi or the greeks for even iventing algebra! lol since i am probably the worst person in my algebra class, i guess i will be coming here more often lo

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Question 170106: Someone should sue al-khwarizmi or the greeks for even iventing algebra! lol
since i am probably the worst person in my algebra class, i guess i will be coming here more often lol
if someone could help me with these three problems id be very thankful =)
(x+2)(x+3)= x^2+2x+3x+6= 11x^4 (or not?)

(2x-5)(3x+2) (my teacher olny wrote to that; "you should use the foil system")
(2x+5)(x^2-x-2) (I got that one totally wrong, but that was only because i didnt really understand it at all).

Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

You are on the right track, but combined the terms incorrectly.


Remember, you can only combine terms if they have the same variable AND the same exponent. So you CANNOT combine the terms x%5E2 and 2x. Likewise, you CANNOT combine 3x and 6 (since they are not like terms).


This means that...


%28x%2B2%29%28x%2B3%29=+x%5E2%2B2x%2B3x%2B6+=+x%5E2%2B5x%2B6


So %28x%2B2%29%28x%2B3%29=x%5E2%2B5x%2B6




# 2

%282x-5%29%283x%2B2%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%282x%29-5%29%28highlight%283x%29%2B2%29 Multiply the First terms:%282%2Ax%29%2A%283%2Ax%29=6x%5E2.


%28highlight%282x%29-5%29%283x%2Bhighlight%282%29%29 Multiply the Outer terms:%282%2Ax%29%2A%282%29=4x.


%282x%2Bhighlight%28-5%29%29%28highlight%283x%29%2B2%29 Multiply the Inner terms:%28-5%29%2A%283%2Ax%29=-15x.


%282x%2Bhighlight%28-5%29%29%283x%2Bhighlight%282%29%29 Multiply the Last terms:%28-5%29%2A%282%29=-10.


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


6x%5E2%2B4x-15x-10 Now collect every term to make a single expression.


6x%5E2-11x-10 Now combine like terms.


So %282x-5%29%283x%2B2%29 FOILs to 6x%5E2-11x-10.


In other words, %282x-5%29%283x%2B2%29=6x%5E2-11x-10.




# 3


%282x%2B5%29%28x%5E2-x-2%29 Start with the given expression.


2x%28x%5E2-x-2%29%2B5%28x%5E2-x-2%29 Expand. Remember, %28a%2Bb%29%28c%2Bd%2Be%29=a%28c%2Bd%2Be%29%2Bb%28c%2Bd%2Be%29


Distribute.


2x%5E3-2x%5E2-4x%2B5x%5E2-5x-10 Multiply.


2x%5E3%2B3x%5E2-9x-10 Now combine like terms.


So %282x%2B5%29%28x%5E2-x-2%29 expands to 2x%5E3%2B3x%5E2-9x-10.


In other words, %282x%2B5%29%28x%5E2-x-2%29=2x%5E3%2B3x%5E2-9x-10.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Sue the deceased? That's a novel notion!
In your first problem, you have successfully used the FOIL method to multiply the two binomials.
%28x%2B2%29%28x%2B3%29+=+x%5E2%2B2x%2B3x%2B6 but you cannot simply add all of these terms together as you have apparently done! Try adding Pesos and Dollars together!
What you must do is combine the LIKE-TERMS, that is, add the terms together that have something in common with each other, like terms with x's only or, terms with constants only.
x%5E2%2Bhighlight%282x%2B3x%29%2B6+=+x%5E2%2B5x%2B6
----------------------------------------
Multiply, using the FOIL method: FOIL means First, Outer, Inner, Last, and this indicates the order in which you are to multiply the terms of the two binomials.
Now perform the multiplication indicated in each term:
Finally, combine the like-terms.
highlight%286x%5E2-11x-10%29
--------------------------------
Multiply, using the FOIL method:
Perform the indicated multiplication.
=highlight%282x%5E3%2B3x%5E2-9x-10%29