Q. 6.71 - Intermediate Algebra

Question

Factor completely:$16x^3-36x$

Step-by-Step Solution

Answer

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

Step 1. Given Information

The given expression is $16x^3-36x$

Step 2. Calculation

We will first take out the common factor out and they apply the property to find the required factors.

$$\begin{gathered} 16x^3-36x=4x(16x^2-9) \\ =4x({\left(4x\right)}^2-{\left(3\right)}^2) \\ =4x(4x-3)(4x+3) \end{gathered}$$

Step 3. Check

We will check the obtained factors by multiplying them.

$$\begin{gathered} 4x(4x-3)(4x+3)=4x({\left(4x\right)}^2-{\left(3\right)}^2) \\ =4x(16x^2-9) \\ =16x^3-36x \end{gathered}$$