`~rai~`
\(a)8x^2-8xy-4x+4y\\=(8x^2-8xy)-(4x-4y)\\=8x(x-y)-4(x-y)\\=4(x-y)(2x-1).\\b)x^3+10x^2+25x-xy^2\\=x(x^2+10x+25-y^2)\\=x\left[(x^2+10x+25)-y^2\right]\\=x[(x+5)^2-y^2]\\=x(x+5+y)(x+5-y).\\c)x^2+x-6\\=x^2-2x+3x-6\\=(x^2-2x)+(3x-6)\\=x(x-2)+3(x-2)\\=(x-2)(x+3).\\d)2x^2+4x-16\\=2(x^2+2x-8)\\=2(x^2-2x+4x-8)\\=2\left[(x^2-2x)+(4x-8)\right]\\=2\left[x(x-2)+4(x-2)\right]\\=2(x-2)(x+4).\)