Question

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

Answer 1

Answer:

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Answer 2

Factors of $\bf {(2y + x)}^{2} (y - 2x) + {(2x + y)}^{2} (2x - y)$ are $\bf \red{ 3(y - 2x)( x + y) (y - x )}$.

Given:

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

To find:

• Factors of polynomial.

Solution:

Identity to be used:

$\bf ( {a}^{2} - {b}^{2} ) = (a + b)(a - b)$

Step 1:

Take (-1) common from last term.

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

or

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

take (y-2x) from both terms.

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

Step 2:

Compare the inner bracket with identity.

It is clear that

$a = 2y + x$

and

$b = 2x + y$

apply Identity.

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

or

$= (y - 2x)(3 x + 3 y) (y - x )$

or

$= 3(y - 2x)( x + y) (y - x )$

Thus,

Factors of $\bf {(2y + x)}^{2} (y - 2x) + {(2x + y)}^{2} (2x - y)$ are $\bf 3(y - 2x)( x + y) (y - x )$.

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