Finite Math Examples

$f (x) = 8 x^{3} + 1$

Step 1

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

$f (x) = {(2 x)}^{3} + 1$

Step 2

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

$f (x) = {(2 x)}^{3} + 1^{3}$

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 $a = 2 x$ and $b = 1$ .

$f (x) = (2 x + 1) ({(2 x)}^{2} - 2 x \cdot 1 + 1^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $2 x$ .

$f (x) = (2 x + 1) (2^{2} x^{2} - 2 x \cdot 1 + 1^{2})$

Step 4.2

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

$f (x) = (2 x + 1) (4 x^{2} - 2 x \cdot 1 + 1^{2})$

Step 4.3

Multiply $2$ by $- 1$ .

$f (x) = (2 x + 1) (4 x^{2} - 2 x \cdot 1 + 1^{2})$

Step 4.4

Multiply $- 2$ by $1$ .

$f (x) = (2 x + 1) (4 x^{2} - 2 x + 1^{2})$

Step 4.5

One to any power is one.

$f (x) = (2 x + 1) (4 x^{2} - 2 x + 1)$