Factoring Sum and Difference of Two Cubes Practice Problems ... - Free Printable

Final Answer:
$ 2(x - 2)(x^2 + 2x + 4) $

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Explanation:
We start with the expression:
$ 2x^3 - 16 $

Step 1: Factor out the common factor 2:
$ 2x^3 - 16 = 2(x^3 - 8) $

Step 2: Notice that $ x^3 - 8 $ is a difference of cubes, because $ 8 = 2^3 $.
The formula for difference of cubes is:
$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) $

Here, $ a = x $, $ b = 2 $, so:
$ x^3 - 2^3 = (x - 2)(x^2 + x\cdot2 + 2^2) = (x - 2)(x^2 + 2x + 4) $

Step 3: Put the 2 back in front:
$ 2(x - 2)(x^2 + 2x + 4) $

That’s the fully factored form — and the green checkmark confirms it’s correct!