Question

Factor completely:$27y^2-48$

Short answer

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

Step-by-step solution

Step 1. Given Information

The given expression is$27y^2-48$

Step 2. Calculation

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

$$\begin{gathered} 27y^2-48=3(9y^2-16) \\ =3({\left(3y\right)}^2-{\left(4\right)}^2) \\ =3(3y-4)(3y+4) \end{gathered}$$

Step 3. Check

We will check the obtained factors by multiplying them.

$$\begin{gathered} 3(3y-4)(3y+4)=3({\left(3y\right)}^2-{\left(4\right)}^2) \\ =27y^2-48 \end{gathered}$$