SOLUTION: Q1= if 3 a^2 = b^2 (≠) 0 , then the value of [(a+b)^3-(a-b)^3]/[(a+b)^2+(a-b)^2]

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Question 926191: Q1= if 3 a^2 = b^2 (≠) 0 , then the value of
[(a+b)^3-(a-b)^3]/[(a+b)^2+(a-b)^2]
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28a%2Bb%29%5E3-%28a-b%29%5E3%29%2F%28%28a%2Bb%29%5E2%2B%28a-b%29%5E2%29

Factor the numerator as the difference of two cubes.
Square out the terms in the denominator



Continue simplifying:



2b%283a%5E2%2Bb%5E2%29%2F%282%28a%5E2%2Bb%5E2%29%29

cross%282%29b%283a%5E2%2Bb%5E2%29%2F%28cross%282%29%28a%5E2%2Bb%5E2%29%29

b%283a%5E2%2Bb%5E2%29%2F%28a%5E2%2Bb%5E2%29

or

b%283a%5E2%2Bb%5E2%29%22%F7%22a%5E2%2Bb%5E2

Now since 3a%5E2+=+b%5E2

We can either give the final answer in terms of either a or b.

If we substitute b%5E2 for 3a%5E2 and thus b%5E2%2F3 for a%5E2,

in

b%283a%5E2%2Bb%5E2%29%22%F7%22a%5E2%2Bb%5E2, we get:

b%28b%5E2%2Bb%5E2%29%22%F7%22%28b%5E2%2F3%2Bb%5E2%29

b%282b%5E2%29%22%F7%22%28b%5E2%2F3%2B3b%5E2%2F3%29

%282b%5E3%29%22%F7%22%284b%5E2%2F3%29

%282b%5E3%29%22%D7%22%283%2F%284b%5E2%29%29

%286b%5E3%2F%284b%5E2%29%29

3b%2F2  <--- that is the answer in terms of b

Ifyou want the answer in terms of a, solve for b

3a%5E2+=+b%5E2

%22%22+%2B-+sqrt%283a%5E2%29=b

%22%22+%2B-+a%2Asqrt%283%29=b

Then  3b%2F2 becomes

%22%22+%2B-+3a%2Asqrt%283%29%2F2   <--- that is the answer in terms of a

Edwin