Question

factorise (x-2y)^2+8xy

Answer 1

Given (x-2y)^2 + 8xy can be written as

We know that (a-b)^2 = a^2 + b^2 - 2ab.

           x^2 + 2y^2 - 4xy + 8xy

           x^2 + 2y^2 + 4xy

           (x + 2y)^2.


Hope this helps!

Answer 2

Concept:

Factorization of a polynomial can be defined as the converting of the equation to a product of factors that cannot be reduced further.

Given:

The equation (x-2y)² + 8xy.

Find:

Factorization of the given equation (x-2y)² + 8xy.

Solution:

Using the equation (a-b)² = a² + b² - 2ab expanding,

(x-2y)² + 8xy = x² + 4y² - 4xy + 8xy

(x-2y)² + 8xy = x² + (2y)²- (2)(2)xy + 8xy

(x-2y)² + 8xy = x² + 4y² + 4xy

It is observed that the equation x² + y² + 4xy resembles to (a+b)² = a² + b² + 2ab.

So, x² + 4y² + 4xy = (x+2y)²

So, (x-2y)² + 8xy = (x+2y)²

(x-2y)² + 8xy = (x+2y)(x+2y)

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

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