Question

Simplify the following (a+b)^2 + (a-b)^2

Answer 1

We simply use algebraic identities here.

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

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

= 2 ( a ^ 2 + b ^ 2)

= 2 a ^ 2 + 2 b ^ 2

Answer 2

Answer:

The simplified form of the given expression is $2(a^2+b^2)$.

Step-by-step explanation:

The given expression is

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

Using algebraic formulas:

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

Combine like terms.

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

$(a+b)^2+(a-b)^2=2a^2+0+2b^2$

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

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

Therefore the simplified form of the given expression is $2(a^2+b^2)$.