Q. 199 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$8-343t^3$

Step-by-Step Solution

Answer

The factored form of the given expression is $(2-7t)(4+14t+49t^2)$.

Step 1. Given information.

The given expression is:

$8-343t^3$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}8-343t^3& =& 2^3-{\left(7t\right)}^3 \\ & =& (2-7t)(2^2+(2\left)\right(7t)+{\left(7t\right)}^2) \left[\because a^3-b^3=(a-b)(a^2+ab+b^2)\right]\\ & =& (2-7t)(4+14t+49t^2)\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(2-7t)(4+14t+49t^2)$.