Question

a)x\(^2\)-6x-y\(^2\)+9

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

c)x\(^2\)-4xy+4y\(^2\)-z\(^2\)-4zt-4t\(^2\)

Answer 1

\(a)x^2-6x-y^2+9\)

\(=x^2-6x+9-y^2\)

\(=\left(x-3\right)^2-y^2\)

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

Answer 2

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

Answer 3

\(c)x^2-4xy+4y^2-z^2-4zt-4t^2\)

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

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