Math, asked by bhavanikannan1981, 2 months ago

find the value of (2x+y)²-(2x-y)²

Answers

Answered by ankushsaini23

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${x}^{2} - {y}^{2} = (x + y)(x - y)$

Therefore,

$= ( {2x + y)}^{2} - {(2x - y)}^{2}$

$= (2x + y + 2x - y)(2x + y - 2x + y)$

$= (4x)(2y)$

$= 8xy$

Answered by HanitaHImesh

Given,

The expression: (2x+y)²-(2x-y)².

To find,

The value of the given expression.

Solution,

The value of (2x+y)²-(2x-y)² will be 8xy.

According to the question,

The expression: (2x+y)²-(2x-y)².

Expanding this expression using the identity: (a²-b²) = (a+b)(a-b),

(Note that in this case, a = 2x+y and b = 2x-y).

(2x+y)²-(2x-y)²

(2x+y+2x-y) (2x+y-2x+y)

4x (2y)

8xy

Hence, the value of (2x+y)²-(2x-y)² is 8xy.

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