Q. 6.86 - Intermediate Algebra

Question

Factor completely: $16x^2-24xy+9y^2-64$

Step-by-Step Solution

Answer

The required factors are $(4x-3y-8)(4x-3y+8)$

Step 1. Given Information

The given expression is $16x^2-24xy+9y^2-64$

Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis and then use the property.

$$\begin{gathered} 16x^2-24xy+9y^2-64={\left(4x\right)}^2-2\times 4x\times 3y+{\left(3y\right)}^2-64 \\ ={[4x-3y]}^2-8^2 \\ =(4x-3y-8)(4x-3y+8) \end{gathered}$$

Step 3. Check

We will verify by multiplying the factors.

$$\begin{gathered} (4x-3y-8)(4x-3y+8)={[4x-3y]}^2-8^2 \\ ={\left(4x\right)}^2-2\times 4x\times 3y+{\left(3y\right)}^2-64 \\ =16x^2-24xy+9y^2-64 \end{gathered}$$