Q. 206 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$6x^3-48y^3$

Step-by-Step Solution

Answer

The factored form of the given expression is $6(x-2y)(x^2+2xy+4y^2)$.

Step 1. Given information.

The given expression is:
$6x^3-48y^3$

Step 2. Determine the factored form.

The given expression can be written as:

$\begin{array}{rcl}6x^3-48y^3& =& 6(x^3-8y^3)\\ & =& 6(x^3-{\left(2y\right)}^3) \\ & =& 6(x-2y)(x^2+(x\left)\right(2y)+{\left(2y\right)}^2) \left[\because a^3-b^3=(a-b)(a^2+ab+b^2\right]\\ & =& 6(x-2y)(x^2+2xy+4y^2)\end{array}$

Step 3. Conclusion.

The factored form of the given expression $6(x-2y)(x^2+2xy+4y^2)$.