Factor 216e^3-1

$216 e^{3} - 1$

Step 1

Rewrite $216 e^{3}$ as ${(6 e)}^{3}$ .

${(6 e)}^{3} - 1$

Step 2

Rewrite $1$ as $1^{3}$ .

${(6 e)}^{3} - 1^{3}$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 6 e$ and $b = 1$ .

$(6 e - 1) ({(6 e)}^{2} + 6 e \cdot 1 + 1^{2})$

Step 4

Simplify.

Apply the product rule to $6 e$ .

$(6 e - 1) (6^{2} e^{2} + 6 e \cdot 1 + 1^{2})$

Raise $6$ to the power of $2$ .

$(6 e - 1) (36 e^{2} + 6 e \cdot 1 + 1^{2})$

Multiply $6$ by $1$ .

$(6 e - 1) (36 e^{2} + 6 e + 1^{2})$

One to any power is one.

$(6 e - 1) (36 e^{2} + 6 e + 1)$

Factor 216e^3-1

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