(x-y) ² - 7 (x² - y²) + 12 (x+y)
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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^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)}
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