Q. 403 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.

$2m^3+54$

Step-by-Step Solution

Answer

The simplified factor is $2(m+3)(m^2-3m+9)$

Step 1. Given information.

The polynomial expression given is

$2m^3+54$.

To find factor using sum and difference of cube following formula are used,

$$\begin{gathered} (a^3-b^3)=(a-b)(a^2+ab+b^2) \\ (a^3+b^3)=(a+b)(a^2-ab+b^2) \end{gathered}$$

Step 2. Calculate the expression.

$$\begin{gathered} 2m^3+54=2(m^3+27) \\ =2({\left(m\right)}^3+3^3) \\ =2(m+3)(m^2-3m+9) \end{gathered}$$