Q. 404 - Intermediate Algebra

Question

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

$81m^3+3$

Step-by-Step Solution

Answer

The simplified factor is $3(3m+1)(9m^2-3m+1)$

Step 1. Given information.

The polynomial expression given is

$81m^3+3$.

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.

$$\begin{gathered} 81m^3+3=3(27m^3+1) \\ =3({\left(3m\right)}^3+1^3) \\ =3(3m+1)(9m^2-3m+1) \end{gathered}$$