Q 55E - Intermediate Algebra

Question

In the following exercises, factor.

$x^2+xy+5x+5y$.

Step-by-Step Solution

Answer

The obtained factors for the expression $x^2+xy+5x+5y$ are,$\left(x+y\right)\left(x+5\right)$.

Step 1 Given expression is,

$x^2+xy+5x+5y$.

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

Step 2 First group each term with the common factors.

$x^2+xy+5x+5y=\left(x^2+xy\right)+\left(5x+5y\right)$

Now factor out the common terms.

$$\begin{gathered} x^2+xy+5x+5y=x\left(x+y\right)+5\left(x+y\right) \\ =\left(x+y\right)\left(x+5\right) \end{gathered}$$

The obtained factors are,$\left(x+y\right)\left(x+5\right)$.

Step 3 let us check the answer by multiplying the factors.

$$\begin{gathered} \left(x+y\right)\left(x+5\right)=x^2+5x+xy+5y \\ =x^2+xy+5x+5y \end{gathered}$$

which is true.