Question

a) \(\left(x-9\right)\left(x-7\right)+1\)

b)\(\left(x^2+x-1\right)^2+4x^2+4x\)

c) \(\left(x+2y-3\right)^2-4\left(x+2y-3\right)+4\)

d)\(\left(x-y\right)^3-1-3\left(x-y\right)\left(x-y-1\right)\)

Answer 1

a)\(=\left(x^2-7x-9x+63\right)+1\)

\(=x^2-7x-9x+63+1\)

=\(x^2-16x+64\)

\(=\left(x-8\right)^2\)

Answer 2

a: \(=x^2-16x+63+1\)

\(=x^2-16x+64=\left(x-8\right)^2\)

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

\(=\left(x^2+x\right)^2+2\left(x^2+x\right)+1\)

\(=\left(x^2+x+1\right)^2\)

c: \(=\left(x+2y-3-2\right)^2\)

\(=\left(x+2y-5\right)^2\)

d: \(=\left(x-y\right)^3-1-3\left(x-y\right)^2+3\left(x-y\right)\)

\(=\left(x-y-1\right)^3\)