Algebra Examples

$27 u^{3} + 64$

Step 1

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

${(3 u)}^{3} + 64$

Step 2

Rewrite $64$ as $4^{3}$ .

${(3 u)}^{3} + 4^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 3 u$ and $b = 4$ .

$(3 u + 4) ({(3 u)}^{2} - (3 u) \cdot 4 + 4^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the product rule to $3 u$ .

$(3 u + 4) (3^{2} u^{2} - (3 u) \cdot 4 + 4^{2})$

Step 4.2

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

$(3 u + 4) (9 u^{2} - (3 u) \cdot 4 + 4^{2})$

Step 4.3

Multiply $3$ by $- 1$ .

$(3 u + 4) (9 u^{2} - 3 u \cdot 4 + 4^{2})$

Step 4.4

Multiply $4$ by $- 3$ .

$(3 u + 4) (9 u^{2} - 12 u + 4^{2})$

Step 4.5

Raise $4$ to the power of $2$ .

$(3 u + 4) (9 u^{2} - 12 u + 16)$