Question

Solve: (x+y)^2- (x-y)^2

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Answer 1

$\huge\bf\underline{Question:}$

Solve: ${(x + y)}^{2} - {(x - y)}^{2}$

$\huge\bf\underline{Solution:}$

${(x + y)}^{2} - {(x - y)}^{2} \\ {x }^{2} + 2xy + {y}^{2} - ( {x}^{2} - 2xy + {y}^{2} ) \\ {x}^{2} + 2xy + {y}^{2} - {x}^{2} + 2xy - {y}^{2} \\ = 4xy$

Answer 2

Let (x + y ) = a and (x- y ) = b

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

(x + y + x -y ) × (x + y -(x -y ) )

( a^2 - b^2 ) = (a +b) × (a -b)

thus = (2x) × (2y ) = 4xy