Question

(3x-4y)^2-(2x-3y)^2 find factorise

Answer 1

Hi friend
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Your answer
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FACTORISATION
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(3x - 4y)² - (2x - 3y)²

= (3x - 4y + 2x - 3y) ( 3x - 4y - 2x + 3y). [using identity a² - b² = (a + b)(a - b)]

= (5x - 7y)(x - y)

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Answer 2

The factors of $( {3x - 4y)}^{2} - ( {2x - 3y)}^{2}$ are $\bf \red{(5x - 7y)(x - y)}$.

Given:

• An algebraic expression $( {3x - 4y)}^{2} - ( {2x - 3y)}^{2}$

To find:

• Find the factors of expression.

Solution:

Identity to be used:

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

Step 1:

Compare the given expression with identity and identify a and b.

It is clear that

$\bf a = 3x - 4y$

and

$\bf b = 2x - 3y$

Step 2:

Apply identity to factorise.

$( {3x - 4y)}^{2} - ( {2x - 3y)}^{2} = (3x - 4y + 2x - 3y)(3x - 4y - 2x + 3y)$

or

$\bf ( {3x - 4y)}^{2} - ( {2x - 3y)}^{2} = (5x - 7y)(x - y )$

Thus,

Factors are (5x-7y)(x-y).

By this way using Identity we can easily factorise this type of expression.

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