Question

factorise 2(x-2y)^2-50y^2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\bf \red{2( {x - 2y)}^{2} - 50 {y}^{2} = 2(x + 3y)(x - 7y)}$

Given:

• $2( {x - 2y)}^{2} - 50 {y}^{2}$

To find:

• Factorize the polynomial.

Solution:

• Take common factor.
• Apply Identity $( {a}^{2} - {b}^{2} ) = (a - b)(a + b)$

Step 1:

Rewrite the polynomial.

$2( {x - 2y)}^{2} - 50 {y}^{2} = 2(( {x - 2y)}^{2} - ( {5y)}^{2})$

Compare the expression with the Identity.

$\bf {a}^{2} = ( {x - 2y)}^{2}$

and

$\bf {b}^{2} = {(5y)}^{2}$

Step 2:

Factorize the polynomial.

$2(( {x - 2y)}^{2} - ( {5y)}^{2}) = 2(x - 2y + 5y)(x - 2y - 5y)$

or

$= 2(x + 3y)(x - 7y)$

Thus,

$\bf 2( {x - 2y)}^{2} - 50 {y}^{2} = 2(x + 3y)(x - 7y)$

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