Q. 195 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$x^3+125$

Step-by-Step Solution

Answer

The factored form of the given expression is $(x+5)(x^2-5x+25)$.

Step 1. Given information.

The given expression is:
$x^3+125$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}{x}^3+125& =& x^3+5^3\\ & =& (x+5)(x^2-(x\left)\right(5)+5^2) \left[\because a^3+b^3=(a+b)(a^2-ab+b^2)\right]\\ & =& (x+5)(x^2-5x+25)\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(x+5)(x^2-5x+25)$.