a) \(a\left(x-y\right)+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(a-b\right)\left(x-y\right)\)
\(a,a\left(x-y\right)+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(a+b\right)\left(x-y\right)\)
\(b,ac+bc+a+b\)
\(=\left(a+b\right)c+\left(a+b\right)\)
\(\left(a+b\right)\left(c+1\right)\)
\(c,5x^2-5ax-7a+7x\)
\(=5x\left(x-a\right)-7\left(a-x\right)\)
\(=5x\left(x-a\right)+7\left(x-a\right)\)
\(=\left(5x+7\right)\left(x-a\right)\)
\(d,7z^2-7yz-4z+4y\)
\(=7z\left(z-y\right)-4\left(z-y\right)\)
\(=\left(7z-4\right)\left(z-y\right)\)
\(e,x^3+3x^2+3x+9\)
\(=\left(x^3+3x^2\right)+\left(3x+9\right)\)
\(=x^2\left(x+3\right)+3\left(x+3\right)\)
\(=\left(x^2+3\right)\left(x+3\right)\)
\(f,x^3-x^2y-x^2z-xyz\)
\(=\left(x^3-x^2y\right)+\left(-x^2z-xyz\right)\)
\(=x^2\left(x-y\right)-xz\left(x-y\right)\)
\(=\left(x^2-xz\right)\left(x-y\right)\)
\(=x\left(x-z\right)\left(x-y\right)\)
\(g,pq-p^2-5\left(p-q\right)\)
\(=\left(pq-p^2\right)-5\left(p-q\right)\)
\(=p\left(q-p\right)+5\left(q-p\right)\)
\(=\left(p+5\right)\left(q-p\right)\)
