Question

(a + b)^2 + (a - b)^2 is equal to​

Answer 1

given :- (a + b)^2 + (a - b)^2

according to algebraic identity,

• (a + b)^2 = a^2 + 2ab + b^2

• (a - b)^2 = a^2 - 2ab + b^2

∴ (a + b)^2 + (a - b)^2 =  (a^2 + 2ab + b^2) + (a^2 - 2ab + b^2)

= a^2 + 2ab + b^2 + a^2 - 2ab + b^2

= a^2 + a^2 + b^2 + b^2 + 2ab - 2ab

= 2a^2 + 2b^2

hence, (a + b)^2 + (a - b)^2 is equal to 2a^2 + 2b^2

Answer 2

Solution:-

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

As, we know that

(a+b)²= a²+2ab+b² -(1)

and,

(a-b)²= a²-2ab+b² -(2)

Using equation -(1) and -(2)

$\bold{ = (a {}^{2} + 2ab + b {}^{2} ) + (a {}^{2} - 2ab + b {}^{2} )}$

$= \bold{a {}^{2} + \cancel{ 2ab} + b {}^{2} + a {}^{2} - \cancel{2ab }+ b {}^{2} }$

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

$\huge \bold \red{= 2(a {}^{2} + b {}^{2} )}$