Question

g)  27 + 27x + 9x² + x³;                              i) 2x² + 2y² - x²z + z - y²z - 2

k) 8 - 27x³                                                  l ) 3x² - 6xy + 3y²

Answer 1

k: \(=\left(2-3x\right)\left(4+6x+9x^2\right)\)

i: \(=3\left(x^2-2xy+y^2\right)=3\left(x-y\right)^2\)

Answer 2

\(g,27+27x+9x^2+x^3=\left(3+x\right)^3\\ i,2x^2+2y^2-x^2z+z-y^2z-2=\left(2x^2-x^2z\right)+\left(2y^2-y^2z\right)-\left(2-z\right)=x^2\left(2-z\right)+y^2\left(2-z\right)-\left(2-z\right)=\left(x^2+y^2-1\right)\left(2-z\right)\)

\(k,8-27x^2=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)

\(l,3x^2-6xy+3y^2=3\left(x^2-2xy+y^2\right)=3\left(x-y\right)^2\)