Question

divide by factorisation method( 3-12(x-y)square by (1-2x+2y)

Answer 1

SOLUTION

TO DETERMINE

By factorisation method

$\displaystyle \sf{ \frac{3 - 12 {(x - y)}^{2} }{(1 - 2x + 2y)} \: }$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

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

EVALUATION

$\displaystyle \sf{ \frac{3 - 12 {(x - y)}^{2} }{(1 - 2x + 2y)} \: }$

$= \displaystyle \sf{ \frac{3 \bigg[1 - 4 {(x - y)}^{2} \bigg] }{(1 - 2x + 2y)} \: }$

$= \displaystyle \sf{ \frac{3 \bigg[1 - {(2x - 2y)}^{2} \bigg] }{(1 - 2x + 2y)} \: }$

$= \displaystyle \sf{ \frac{3 (1 + 2x - 2y)(1 - 2x + 2y)}{(1 - 2x + 2y)} \: } \:( by \: above \: identity)$

$= \sf{3(1 + 2x - 2y) \: }$

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