How to prove (a /2+ b)^2(a /2- b)^2= ab​

Question

How to prove (a /2+ b)^2(a /2- b)^2=

ab​

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Gabriella 1 month 2021-08-21T22:25:28+00:00 1 Answer 0 views 0

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    2021-08-21T22:26:58+00:00

    Answer:

    We can show that the right side of the equation is equal to the left side, by expanding it out and then factorising:

    ( a+b)2+(a−b)2

    = (a+b)(a+b)+(a−b)(a−b)

    = (a2+ab+ab+b2)+(a2−ab−ab+b2)

    = a2+2ab+b2+a2−2ab+b2

    = 2a2+2b2

    = 2(a2+b2)

    Therefore, it is shown that

    2(a2+b2)=(a+b)2+(a−b)2

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