Q 51E - Intermediate Algebra

Question

In the following exercises, factor.

$-18x{y}^2- 27x^2 y$.

Step-by-Step Solution

Answer

The obtained factor for the expression$-18x{y}^2- 27x^2 y$ is,$-9xy\left(2y+3x\right)$.

Step 1 The given expression is,

$-18x{y}^2- 27x^2 y$.

The objective is, we need to find the factors for the given expression.

Step 2 First find the GCF for the given expression.

$$\begin{gathered} -18x{y}^2=-9\times 2\times x\times y\times y \\ - 27x^2 y=-9\times 3\times x\times x\times y \end{gathered}$$

The GCF $=-9xy$

Step 3 In the given expression rewrite each term using the GCF.

$-18x{y}^2- 27x^2 y=-9xy\left(2y\right)+\left(-9xy\right)\left(3x\right)$

Now factor out the GCF.

$-18x{y}^2- 27x^2 y=-9xy\left(2y+3x\right)$

The obtained factor is,$-9xy\left(2y+3x\right)$.

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

$-9xy\left(2y+3x\right)=-18x{y}^2-27x^{2}y$

which is true.