Q. 204 - Intermediate Algebra

Question

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

$27y^3+8z^3$

Step-by-Step Solution

Answer

The factored form of the given expression is $(3y+2z)(9y^2-6yz+4z^2)$.

Step 1. Given information.

The given expression is:

$27y^3+8z^3$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}27y^3+8z^3& =& {\left(3y\right)}^3+{\left(2z\right)}^3\\ & =& (3y+2z)({\left(3y\right)}^2-(3y\left)\right(2z)+{\left(2z\right)}^2) \left[\because a^3+b^3=(a+b)(a^2-ab+b^2)\right]\\ & =& (3y+2z)(9y^2-6yz+4z^2)\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(3y+2z)(9y^2-6yz+4z^2)$.