Q. 6.74 - Intermediate Algebra

Question

Factor completely: $9x^2-24xy+16y^2$

Step-by-Step Solution

Answer

The required factors are ${(3x-4y)}^2$

Step 1. Given Information

The given expression is $9x^2-24xy+16y^2$

Step 2. Calculation

We will factor the expression by using the property. 

$$\begin{gathered} 9x^2-24xy+16y^2={\left(3x\right)}^2-2\times 3x\times 4y+{\left(4y\right)}^2 \\ ={(3x-4y)}^2 \end{gathered}$$

Step 3. Check

We will verify the obtained factors by multiplying them.

$$\begin{gathered} {(3x-4y)}^2={\left(3x\right)}^2-2\times 3x\times 4y+{\left(4y\right)}^2 \\ =9x^2-24xy+16y^2 \end{gathered}$$