Question

factorise 225x^2-9x^2-36y^2+36xy​

Answer 1

Answer:

This is your answer

Hope this is helpful for you...

Answer 2

Factors are $\bf \red{225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = 36(3x - y)(2x + y)}$

Given:

• $225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy$

To find:

• Find the factors of given polynomial.

Solution:

Identity to be used:

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

Step 1:

Take (-) common from last three terms and rewrite the terms.

$225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = 225 {x}^{2} - ( \red{ {(3x)}^{2} + {(6y)}^{2} - 2(3x)(6y)})$

apply Identity 1 in red colour.

$225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = 225 {x}^{2} - ( {3x - 6y)}^{2}$

Step 2:

Rewrite the polynomial and apply Identity 2.

$225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = {(15x)}^{2} - ( {3x - 6y)}^{2}$

Here

$\bf a = 15x$

and

$\bf b = 3x - 6y$

so,

${(15x)}^{2} - ( {3x - 6y)}^{2} = (15x + 3x - 6y)(15x - 3x + 6y)$

or

$= (18x - 6y)(12x + 6y)$

take common 6 from both factors.

$225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = 36(3x - y)(2x + y)$

Thus,

Factors are

$\bf \: 225 {x}^{2} - 9 {x}^{2} - 36 {y}^{2} + 36xy = 36(3x - y)(2x + y)$

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