Question

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

ab​

Answer 1

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