Question

Fatore : $\frac{ x^{2}- y^{2}-8x+16 }{2x-2y-8}$

Answer 1

$\frac{x^2-y^2-8x+16}{2x-2y-8} = \frac{x^2-8x+16-y^2}{2(x-y-4)} = \frac{(x-4)^2-y^2}{2\cdot(x-4-y)} = \frac{[(x-4)+y]\cdot[(x-4)-y]}{2\cdot(x-4-y)} \\ \\= \frac{[x-4+y]\cdot[x-4-y]}{2\cdot(x-4-y)} = \frac{(x-4+y)\cdot(x-4-y)}{2\cdot(x-4-y)} =\frac{x-4+y}{2}$