Question

The value of ( a+b)² +(a-b)² is​

Answer 1

(a+b)^2 + ( a-b)^2 = 2(a^2 + b^2 ) .

Step-by-step explanation:

Given , (a+b)^2+ (a-b)^2 = ?

We know that ,

(a+b)^2 = a^2 + b^2 + 2ab ———equation 1

We also know that ,

(a-b)^2 = a^2 + b^2 - 2ab ———equation 2

So, in order to find sum of (a+b)^2 and (a-b)^2 ,

i.e (a+b)^2 + ( a-b) ^2 ,

we need to add equations 1 and 2 .

So , by adding equations 1 and 2 , we get ,

=> (a+b)^2 + (a-b)^2 = a^2 + b^2 + a^2 + b^2

= 2(a^2 + b^2 )

As, ( +2ab ) and (—2ab ) terms get cancelled.

Answer 2

Answer:

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

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

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

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