Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$7k^3+56$

Short answer

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

Step-by-step solution

Step 1. Given information.

The given expression is:
$7k^3+56$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}7k^3+56& =& 7(k^3+8)\\ & =& 7(k^3+2^3)\\ & =& 7(k+2)(k^2-(k\left)\right(2)+2^2)\left[\because a^3+b^3=(a+b)(a^2-ab+b^2)\right]\\ & =& 7(k+2)(k^2-2k+4)\end{array}$

Step 3. Conclusion.

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