Question

25(x+y)^2-36(x-2y)^2 factorise

Answer 1

Answer :

Now,

25 (x + y)² - 36 (x - 2y)²

= {5 (x + y)}² - {6 (x - 2y)}²

= (5x + 5y)² - (6x - 12y)²

= (5x + 5y + 6x - 12y) (5x + 5y - 6x + 12y),

using the identity
a² - b² = (a + b) (a - b)

= (11x - 7y) (17y - x),

which is the required factorization.

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Answer 2

The factors of $\bf 25( {x + y)}^{2} - 36( {x - 2y)}^{2}$ are $\bf (11x - 7y)( 17y - x)$

Given:

• A polynomial.
• $25( {x + y)}^{2} - 36( {x - 2y)}^{2}$

To find:

• Factorise the polynomial.

Solution:

Identity to be used:

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

Step 1:

Write the given polynomial in terms of identity.

$25( {x + y)}^{2} - 36( {x - 2y)}^{2} = {5}^{2} ( {x + y)}^{2} - {6}^{2} ( {x - 2y)}^{2}$

or

$25( {x + y)}^{2} - 36( {x - 2y)}^{2} = ( 5{x +5 y)}^{2} - ( {6x - 12y)}^{2}$

Step 2:

Compare the terms with identity.

$a = 5x + 5y \\ b = 6x - 12y$

Find the factors

$25( {x + y)}^{2} - 36( {x - 2y)}^{2} = (5x + 5y + 6x - 12y)(5x + 5y - 6x + 12y)$

or

$25( {x + y)}^{2} - 36( {x - 2y)}^{2} = (11x - 7y)( - x + 17y)$

or

$\bf 25( {x + y)}^{2} - 36( {x - 2y)}^{2} = (11x - 7y)( 17y - x)$

Thus,

Factors of polynomial are (11x-7y)(17y-x).

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