Pre-Algebra Examples

$64 r^{3} + 1$

Step 1

Rewrite $64 r^{3}$ as ${(4 r)}^{3}$ .

${(4 r)}^{3} + 1$

Step 2

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

${(4 r)}^{3} + 1^{3}$

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 $a = 4 r$ and $b = 1$ .

$(4 r + 1) ({(4 r)}^{2} - (4 r) \cdot 1 + 1^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $4 r$ .

$(4 r + 1) (4^{2} r^{2} - (4 r) \cdot 1 + 1^{2})$

Step 4.2

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

$(4 r + 1) (16 r^{2} - (4 r) \cdot 1 + 1^{2})$

Step 4.3

Multiply $4$ by $- 1$ .

$(4 r + 1) (16 r^{2} - 4 r \cdot 1 + 1^{2})$

Step 4.4

Multiply $- 4$ by $1$ .

$(4 r + 1) (16 r^{2} - 4 r + 1^{2})$

Step 4.5

One to any power is one.

$(4 r + 1) (16 r^{2} - 4 r + 1)$