a) 9x (3x-y) +3y (y-3x)
= 9x(3x-y)-3y(3x-y)
=(3x-y)(9x-3y)
= (3x-y)3(3x-y)
= 3(3x-y)2
b)x3 - 3x2 - 9x + 27
=x3+3x2-6x2-18x+9x+27
= (x3+3x2)-(6x2+18x)+(9x+27)
= x2(x+3)-6x(x+3)+9(x+3)
= (x+3)(x2-6x+9)
=(x+3)(x-3)2
a) \(9x\left(3x-y\right)+3y\left(y-3x\right)=9x\left(3x-y\right)-3y\left(3x-y\right)\)
=\(\left(3x-y\right)\left(9x-3y\right)\)
\(=3\left(3x-y\right)\left(3x-y\right)\)
\(=3\left(3x-y\right)^2\)
b) \(x^3-3x^2-9x+27=\left(x^3-3x^2\right)-\left(9x-27\right)\)
\(=x^2\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-9\right)\)
\(=\left(x-3\right)\left(x-3\right)\left(x+3\right)\)
=\(\left(x-3\right)^2\left(x+3\right)\)
\(\text{a) }9x\left(3x-y\right)+3y\left(y-3x\right)\\ \\ =9x\left(3x-y\right)-3y\left(3x-y\right)\\ \\ =3\left(3x-y\right)\left(3x-y\right)\\ \\ =3\left(3x-y\right)^2\)
\(\text{b) }x^3-3x^2-9x+27\\=\left(x^3-3x^2\right)-\left(9x-27\right) \\=x^2\left(x-3\right)-9\left(x-3\right)\\ \\=\left(x^2-9\right)\left(x-3\right)\\ =\left(x+3\right)\left(x-3\right)\left(x-3\right)\\ \\ =\left(x+3\right)\left(x-3\right)^2\)
a) \(9x\left(3x-y\right)+3y\left(y-3x\right)\)
\(=9x\left(3x-y\right)-3y\left(3x-y\right)\)
\(=\left(9x-3y\right)\left(3x-y\right)\)
b) \(x^3-3x^2-9x+27\)
\(=x^2\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x^2-9\right)\left(x-3\right)\)
\(=\left(x+3\right)\left(x-3\right)\left(x-3\right)\)
\(=\left(x+3\right)\left(x-3\right)^2\)