Question

(iii) (a+b)^2 +(a - b)^2​

Answer 1

(a+b)²+(a-b)²

= (a²+2ab+b²)+(a²-2ab+b²)

= a²+2ab+b²+a²-2ab+b²

= a²+a²+b²+b²

= 2a²-2b²

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Answer 2

The answer of this question is $2(a^{2} +b^{2})$.

Step-by-step explanation:

We are given,

$(a+b)^{2} +(a-b)^{2}$

and we have to solve this to get the answer.

• Formula used

1. $(a+b)^{2} =a^{2} +b^{2} +2ab$
2. $(a-b)^{2} =a^{2} +b^{2} -2ab$

• Solving given equation,

we have,

$(a+b)^{2} +(a-b)^{2}$

for simplifying terms we can take

$A =(a+b)^{2}$     and   $B =(a-b)^{2}$

and we have to find A+B,

Solving A;

$A =(a+b)^{2}$

by using formula(1) we get,

$A=a^{2} +b^{2} +2ab$

Solving B;

$B =(a-b)^{2}$

by using formula(2) we get,

$B=a^{2} +b^{2} -2ab$

now add A and B,

$A+B=a^{2} +b^{2} +2ab+a^{2} +b^{2} -2ab$

          $=a^{2} +b^{2} +a^{2} +b^{2}$

          $=2(a^{2} +b^{2})$

In this way we get the answer of this question as $2(a^{2} +b^{2})$.