SOLUTION: Show: {{{ab = (1/2)((a+b)^2 - (a^2 + b^2))}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Show: {{{ab = (1/2)((a+b)^2 - (a^2 + b^2))}}}      Log On


   

Question 542379: Show:
ab+=+%281%2F2%29%28%28a%2Bb%29%5E2+-+%28a%5E2+%2B+b%5E2%29%29
Found 2 solutions by josmiceli, neatmath:
Answer by josmiceli(19441) About Me  (Show Source):
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

Here we just need to manipulate the right side of the equation:

ab=%281%2F2%29%28%28a%2Bb%29%5E2-%28a%5E2%2Bb%5E2%29%29 given

ab=%281%2F2%29%28%28a%5E2%2B2ab%2Bb%5E2%29-%28a%5E2%2Bb%5E2%29%29 expand right side %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2

ab=%281%2F2%29%28a%5E2%2B2ab%2Bb%5E2-a%5E2-b%5E2%29 simplify

ab=%281%2F2%29%282ab%29 combine like terms

ab=ab cancel the 2's

and you have shown that ab=%281%2F2%29%28%28a%2Bb%29%5E2-%28a%5E2%2Bb%5E2%29%29

I hope this helps!