Q. 198 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$y^3-216$

Step-by-Step Solution

Answer

The factored form of the given expression is $(y-6)(y^2+6y+36)$.

Step 1. Given information.

The given expression is:
$y^3-216$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}{y}^3-216& =& y^3-6^3\\ & =& (y-6)(y^2+(y\left)\right(6)+6^2) \left[\because a^3-b^3=(a-b)(a^2+ab+b^2)\right]\\ & =& (y-6)(y^2+6y+36)\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(y-6)(y^2+6y+36)$.