Pre-Algebra Examples

- 216 x^{3} + 1

$- 216 x^{3} + 1$

Step 1

Factor

- 1

$- 1$ out of

- 216 x^{3} + 1

$- 216 x^{3} + 1$ .

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Step 1.1

Factor

- 1

$- 1$ out of

- 216 x^{3}

$- 216 x^{3}$ .

- (216 x^{3}) + 1

$- (216 x^{3}) + 1$

Step 1.2

Rewrite

1

$1$ as

- 1 (- 1)

$- 1 (- 1)$ .

- (216 x^{3}) - 1 (- 1)

$- (216 x^{3}) - 1 (- 1)$

Step 1.3

Factor

- 1

$- 1$ out of

- (216 x^{3}) - 1 (- 1)

$- (216 x^{3}) - 1 (- 1)$ .

- (216 x^{3} - 1)

$- (216 x^{3} - 1)$

- (216 x^{3} - 1)

$- (216 x^{3} - 1)$

Step 2

Rewrite

216 x^{3}

$216 x^{3}$ as

{(6 x)}^{3}

${(6 x)}^{3}$ .

- ({(6 x)}^{3} - 1)

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

Step 3

Rewrite

1

$1$ as

1^{3}

$1^{3}$ .

- ({(6 x)}^{3} - 1^{3})

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

Step 4

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})

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where

a = 6 x

$a = 6 x$ and

b = 1

$b = 1$ .

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

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to

6 x

$6 x$ .

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

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

Step 5.1.2

Raise

6

$6$ to the power of

2

$2$ .

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

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

Step 5.1.3

Multiply

6

$6$ by

1

$1$ .

- ((6 x - 1) (36 x^{2} + 6 x + 1^{2}))

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

Step 5.1.4

One to any power is one.

- ((6 x - 1) (36 x^{2} + 6 x + 1))

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

- ((6 x - 1) (36 x^{2} + 6 x + 1))

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

Step 5.2

Remove unnecessary parentheses.

- (6 x - 1) (36 x^{2} + 6 x + 1)

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

- (6 x - 1) (36 x^{2} + 6 x + 1)

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