Question

find the value of (x+y)2+(x-y)2​

Answer 1

The value of (x + y)² + ( x - y)² = 2( x² + y² )

Given :

The expression (x + y)² + ( x - y)²

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(x + y)² + ( x - y)²

Step 2 of 2 :

Find the value of the expression

(x + y)² + ( x - y)²

= x² + 2xy + y² + x² - 2xy + y²

= 2x² + 2y²

= 2( x² + y² )

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Answer 2

Answer:

Step-by-step

Using the given identities

(x+y)^2=x^2+2xy^2+y^2   ⇒1

(x-y)^2=x^2-2xy^2-y^2      ⇒2

we get

=x^ 2−2xy+y^ 2+ x^ 2+2xy+y^ 2

= x^ 2+x^ 2+y^ 2+y^ 2

= 2x^ 2+2y^ 2

=2(x+y)^2