Question

factorise:(x-y)²-7(x²-y²)+12(x+y)² (with steps)

Answer 1

x²+y²-2xy-7x²+7y²+12(x²+y²+2xy)
x²+y²-2xy-7x²+7y²+12x²+12y²+24xy
x²-7x²+12x²+y²+7y²+12y²-2xy+24xy
6x²+20y²+22xy
=answer

Answer 2

$\huge\underline\mathfrak{Answer:}$

We have, $\sf{(x-y)^2-7(x^2-y^2)+12(x+y)^2}$

=$\sf{(x-y)^2-7(x-y)(x+y)+12(x+y)^2}$

= $\sf{a^2-7ab+12b^2,}$where x-y = a and x + y = b

= $\sf{a^2-3ab-4ab+12b^2}$

=$\sf{(a^2-3ab)+[-4ab+12b^2]}$

= $\sf{a(a-3b)-4b(a-3b)}$

=$\sf{(a-3b)(a-4b)}$

= [(x-y) - 3(x+y)] [(x-y)-4(x+y)], putting back a = x-y and b =x+y

= $\sf{[x-y-3x-3y][x-y-4x-4y]}$

= $\sf{(-2x-4y)-(-3x-5y)}$

=$\sf{[-(2x+4y)][-(3x+5y)]}$

=$\sf{(2x+4y)(3x+5y)}$

$\bold{\large{\boxed{\sf{\red{2(x+2y)(3x+5y)}}}}}$