Question

Find Factorize of: (x–y)^2+4x​y
​

Answer 1

$\underline{\orange{\bf{\blue{\dag}\:Answer:-}}}$

−4x+4y−y ^ 2

Rearranging:−x^2-y^2-4x+4yx 2 −y 2 −4x+4y

As we know

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

.Now, back to your question.

=(x+y)(x-y)-4(x-y) = (x+y)(x−y)−4(x−y)

= (x+y-4)(x-y) = (x+y−4)(x−y)

Answer 2

$\huge \mathscr{\orange {\underline {\pink{\underline{Answer :-}}}}}$

$\tt{−4x+4y−y²}$

Rearranging:

$\tt{−x²-y²-4x+4yx² − y² −4x+4y}$

As we know

$\tt{a²-b²=(a+b)(a-b)a² −b²}$

$\tt{=(a+b)(a−b)}$

Now, back to your question.

$\tt{=(x+y)(x-y)-4(x-y) }$

$\tt{= (x+y)(x−y)−4(x−y)}$

$\tt{= (x+y-4)(x-y) }$

$\tt{= (x+y−4)(x−y)}$

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