Question

1.x^2(x-1)+16(1-x)

2.81x^2-6yz-9y^2-z^2

3.xz-yz-x^2+2xy-y^2

Answer 1

1) \(x^2\left(x-1\right)+16\left(1-x\right)\)

\(=x^2\left(x-1\right)-16\left(x-1\right)\)

\(=\left(x^2-16\right)\left(x-1\right)\)

\(=\left(x^2-4^2\right)\left(x-1\right)\)

\(=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)

2)\(81x^2-6yz-9y^2-z^2\)

\(=81x^2-9y^2-6yz-z^2=81x^2-\left(9y^2+6yz+z^2\right)=81x^2-\left(\left(3y\right)^2+6yz+z^2\right)\)

\(=81x^2-\left(3y+z\right)^2=\left(9x\right)^2-\left(3y+z\right)^2\)

\(=\left(9x+3y+z\right)\left(9x-\left(3y+z\right)\right)=\left(9x+3y+z\right)\left(9x-3y-z\right)\)

3)\(xz-yz-x^2+2xy+y^2\)

\(=z\left(x-y\right)-\left(x^2-2xy+y^2\right)\)

\(=z\left(x-y\right)-\left(x-y\right)^2=\left(z+x-y\right)\left(x-y\right)\)