SOLUTION: Help! from my 8th grade honors algebra homework... (a+b)^4-(a-b)^4 dad sugested doing (a+b)(a+b)(a+b)(a+b)-(a-b)(a-b)(a-b)(a-b) (a^2+2ab+b^2)(a+b)(a+b)-(a^2-2ab+b^2)(

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Help! from my 8th grade honors algebra homework... (a+b)^4-(a-b)^4 dad sugested doing (a+b)(a+b)(a+b)(a+b)-(a-b)(a-b)(a-b)(a-b) (a^2+2ab+b^2)(a+b)(a+b)-(a^2-2ab+b^2)(      Log On


   

Question 23796: Help! from my 8th grade honors algebra homework...
(a+b)^4-(a-b)^4
dad sugested doing
(a+b)(a+b)(a+b)(a+b)-(a-b)(a-b)(a-b)(a-b)
(a^2+2ab+b^2)(a+b)(a+b)-(a^2-2ab+b^2)(a-b)(a-b)
I'm getting way confused carrying this on... is it the right thing to be doing or will I be spinning my wheels on this path???
Thanks in advance...


Found 2 solutions by Paul, stanbon:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
No acutally this is really simple.
%28a%2Bb%29%5E4-%28a-b%29%5E4
expand the polynomoials
a%5E4%2Bb%5E4-a%5E4%2Bb%5E4 -(-) -->+ (negative times a negative gives positive.)
Simplify --The a%5E4 cancel out
Left with 2b%5E4

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Because it is a difference of two squares
you could factor it as [(a+b)^2+(a-b)^2][(a+b)^2-(a-b)^2]
I'm going to called this [1st part][2nd part].
You can factor the 2nd part because it is the difference
of two squares to get:
[(a+b)+(a-b)][(a+b)-(a-b)]
= [2a][2b]
Now, what about that 1st part?!!
If you expand it you get the following:
(a^2+2ab+b^2)+(a^2-2ab+b^2)
Adding you get 2a^2 + 2b^2
So, putting the pieces together you have:
[2a^2+2b^2][2a}{2b]
I'll let you figure out what you want to
do with that. It can be simplified in
several ways but not significantly.
Cheers,
Stan H.