a) \(=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)
b) \(=y\left(x^2-2xy+y^2\right)=y\left(x-y\right)^2\)
c) \(=\left(x-y\right)^2-9z^2=\left(x-y-3z\right)\left(x-y+3z\right)\)
d) \(=\left(a-b\right)^2-16c^2=\left(a-b-4c\right)\left(a-b+4c\right)\)
a. x3 + 4x2 + 4x
= x(x2 + 4x + 4)
= x(x + 2)2
b. x2y - 2xy2 + y3
= y(x2 - 2xy + y2)
= y(x - y)2
c. x2 - 2xy + y2 - 9z2
= (x2 - 2xy + y2) - 9z2
= (x - y)2 - (3z)2
= (x - y - 3z)(x - y + 3z)
d. a2 - 2ab + b2 - 16c2
= (a2 - 2ab + b2) - 16c2
= (a - b)2 - (4c)2
= (a - b - 4c)(a - b + 4c)
c: \(x^2-2xy+y^2-9z^2\)
\(=\left(x-y\right)^2-9z^2\)
\(=\left(x-y-3z\right)\left(x-y+3z\right)\)
d: \(a^2-2ab+b^2-16c^2\)
\(=\left(a-b\right)^2-16c^2\)
\(=\left(a-b-4c\right)\left(a-b+4c\right)\)
