Question

In the following exercises, factor.

$-4x^3{y}^5-x^2{y}^3+12x{y}^4$.

Short answer

The obtained factor for the expression $-4x^3{y}^5-x^2{y}^3+12x{y}^4$is, $-x{y}^3\left(4x^2{y}^2+x-12y\right)$.

Step-by-step solution

Given expression is,

$-4x^3{y}^5-x^2{y}^3+12x{y}^4$.

The objective is, we need to find the factor for this expression.

Step 2 First find the GCF for the given expression.

$$\begin{gathered} -4x^3{y}^5=-2\times 2\times x\times x\times x\times y\times y\times y\times y\times y \\ -x^2{y}^3=-1\times x\times x\times y\times y\times y \\ 12x{y}^4=2\times 6\times x\times y\times y\times y\times y \end{gathered}$$

The GCF is,$x{y}^3$.

In the given expression, rewrite the each term using GCF.

$-4x^3{y}^5-x^2{y}^3+12x{y}^4=x{y}^3\left(-4x^2{y}^2\right)+x{y}^3\left(-x\right)+x{y}^3\left(12y\right)$

Now factor out the GCF.

$$\begin{gathered} -4x^3{y}^5-x^2{y}^3+12x{y}^4=x{y}^3\left(-4x^2{y}^2-x+12y\right) \\ =-x{y}^3\left(4x^2{y}^2+x-12y\right) \end{gathered}$$

The obtained factor is,$-x{y}^3\left(4x^2{y}^2+x-12y\right)$

Step 4 Let us check the answer by multiplying the factors.

$-x{y}^3\left(4x^2{y}^2+x-12y\right)=-4x^3{y}^5-x^2{y}^3+12x{y}^4$

which is true.