Factorise :
x2−2y+xy−4x^2 - 2y + xy - 4x2−2y+xy−4
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x2−2y+xy−4=(x2−4)−(2y−xy)=(x2−22)−(2y−xy)=(x−2)(x+2)−y(2−x)=(x−2)(x+2)+y(x−2)=(x−2)((x+2)+y)=(x−2)(x+2+y)x^2 - 2y + xy - 4\\[1em] = (x^2 - 4) - (2y - xy)\\[1em] = (x^2 - 2^2) - (2y - xy)\\[1em] = (x - 2)(x + 2) - y(2 - x)\\[1em] = (x - 2)(x + 2) + y(x - 2)\\[1em] = (x - 2)\Big((x + 2) + y\Big)\\[1em] = (x - 2)(x + 2 + y)x2−2y+xy−4=(x2−4)−(2y−xy)=(x2−22)−(2y−xy)=(x−2)(x+2)−y(2−x)=(x−2)(x+2)+y(x−2)=(x−2)((x+2)+y)=(x−2)(x+2+y)
Hence, x2−2y+xy−4=(x−2)(x+2+y)x^2 - 2y + xy - 4 = (x - 2)(x + 2 + y)x2−2y+xy−4=(x−2)(x+2+y).
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