Question

Answer 1

a)\(\left(x-9\right)\left(x-7\right)+1=\left(x-9\right)^2+2\left(x-9\right)+1=\left(x-9+1\right)^2=\left(x-8\right)^2\)

b) \(\left(x+2y-3\right)^2-4\left(x+2y-3\right)+4=\left(x+2y-3-2\right)^2=\left(x+2y-5\right)^2\)

d) \(\left(x^2+y^2-17\right)^2-4\left(xy-4\right)^2=\left(x^2+y^2-17\right)^2-\left(2xy-8\right)^2=\left(x^2+y^2-17-2xy+8\right)\left(x^2+y^2-17+2xy-8\right)=\left[\left(x-y\right)^2-9\right]\left[\left(x+y\right)^2-25\right]=\left(x-y-3\right)\left(x-y+3\right)\left(x+y-5\right)\left(x+y-5\right)\)

Answer 2

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

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

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