Basic Math Examples

$27 p^{3} - 8$

Step 1

Rewrite $27 p^{3}$ as ${(3 p)}^{3}$ .

${(3 p)}^{3} - 8$

Step 2

Rewrite $8$ as $2^{3}$ .

${(3 p)}^{3} - 2^{3}$

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 $a = 3 p$ and $b = 2$ .

$(3 p - 2) ({(3 p)}^{2} + 3 p \cdot 2 + 2^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $3 p$ .

$(3 p - 2) (3^{2} p^{2} + 3 p \cdot 2 + 2^{2})$

Step 4.2

Raise $3$ to the power of $2$ .

$(3 p - 2) (9 p^{2} + 3 p \cdot 2 + 2^{2})$

Step 4.3

Multiply $2$ by $3$ .

$(3 p - 2) (9 p^{2} + 6 p + 2^{2})$

Step 4.4

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

$(3 p - 2) (9 p^{2} + 6 p + 4)$