Q. 6.73 - Intermediate Algebra

Question

Factor completely: $4x^2+20xy+25y^2$

Step-by-Step Solution

Answer

The required factors are ${(2x+5y)}^2$

Step 1. Given Information

The given expression is $4x^2+20xy+25y^2$

Step 2. Calculation

We will factor the expression by using the property.

$$\begin{gathered} 4x^2+20xy+25y^2={\left(2x\right)}^2+2\times 2x\times 5y+{\left(5y\right)}^2 \\ ={(2x+5y)}^2 \end{gathered}$$

Step 3. Check

We will verify the obtained factors by multiplying them.

$$\begin{gathered} {(2x+5y)}^2={\left(2x\right)}^2+2\times 2x\times 5y+{\left(5y\right)}^2 \\ =4x^2+20xy+25y^2 \end{gathered}$$