Question

Factorise the b) sum

Steps needed

Answer 1

Heya User, Here is Your Answer

$4(x - y) {}^{2} - 12(x - y) + 9 \\ using \: a {}^{2} - 2ab + {b}^{2} = {(a - b)}^{2} factor \: the \: expression \\ {2}^{2} (x - y) {}^{2} - 2 \times 2(x - y) \times 3 + {3}^{2} \\ (2(x - y)) {}^{2} - 2 \times 2(x - y) \times 3 + 3 {}^{2} \\ (2(x - y) - 3) {}^{2} \\ (2x - 2y - 3) {}^{2}$
Hope it will help you

Answer 2

(b)

Method - 1:

Given Equation is 4(x - y)^2 - 12(x - y) + 9

= > 4x^2 - 8xy + 4y^2 - 12x + 12y + 9

= > 4x^2 - 4xy - 4xy + 4y^2 - 6x - 6x + 6y + 6y + 9

= > 4x^2 - 4xy - 6x - 4xy + 4y^2 + 6y - 6x + 6y + 9

= > 2x(2x - 2y - 3) - 2y(2x - 2y - 3) - 3(2x - 2y - 3)

= > (2x - 2y - 3)(2x - 2y - 3)

= > (2x - 2y - 3)^2.

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Method - 2:

Given Equation is 4(x - y)^2 - 12(x - y) + 9

= > 4(x - y)^2 - 6(x - y) - 6(x - y) + 9

= > 2(x - y)[2(x - y) - 3] - 3[2(x - y) - 3]

= > [2(x - y) - 3][2(x - y) - 3]

= > (2x - 2y - 3)(2x - 2y - 3)

= > (2x - 2y - 3)^2.

Hope this helps!