Basic Math Examples

$3 b^{3} - 3 b^{2} f - 3 b f^{2} + 3 f^{3}$

Step 1

Factor $3$ out of $3 b^{3} - 3 b^{2} f - 3 b f^{2} + 3 f^{3}$ .

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Step 1.1

Factor $3$ out of $3 b^{3}$ .

$3 (b^{3}) - 3 b^{2} f - 3 b f^{2} + 3 f^{3}$

Step 1.2

Factor $3$ out of $- 3 b^{2} f$ .

$3 (b^{3}) + 3 (- b^{2} f) - 3 b f^{2} + 3 f^{3}$

Step 1.3

Factor $3$ out of $- 3 b f^{2}$ .

$3 (b^{3}) + 3 (- b^{2} f) + 3 (- b f^{2}) + 3 f^{3}$

Step 1.4

Factor $3$ out of $3 f^{3}$ .

$3 (b^{3}) + 3 (- b^{2} f) + 3 (- b f^{2}) + 3 (f^{3})$

Step 1.5

Factor $3$ out of $3 (b^{3}) + 3 (- b^{2} f)$ .

$3 (b^{3} - b^{2} f) + 3 (- b f^{2}) + 3 (f^{3})$

Step 1.6

Factor $3$ out of $3 (b^{3} - b^{2} f) + 3 (- b f^{2})$ .

$3 (b^{3} - b^{2} f - b f^{2}) + 3 (f^{3})$

Step 1.7

Factor $3$ out of $3 (b^{3} - b^{2} f - b f^{2}) + 3 (f^{3})$ .

$3 (b^{3} - b^{2} f - b f^{2} + f^{3})$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$3 ((b^{3} - b^{2} f) - b f^{2} + f^{3})$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$3 (b^{2} (b - 1 f) - f^{2} (b - f))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $b - 1 f$ .

$3 ((b - 1 f) (b^{2} - f^{2}))$

Step 4

Rewrite $- 1 f$ as $- f$ .

$3 ((b - f) (b^{2} - f^{2}))$

Step 5

Factor.

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Step 5.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = b$ and $b = f$ .

$3 ((b - f) ((b + f) (b - f)))$

Step 5.2

Remove unnecessary parentheses.

$3 ((b - f) (b + f) (b - f))$

Step 6

Factor.

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Step 6.1

Combine exponents.

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Step 6.1.1

Raise $b - f$ to the power of $1$ .

$3 ({(b - f)}^{1} (b - f) (b + f))$

Step 6.1.2

Raise $b - f$ to the power of $1$ .

$3 ({(b - f)}^{1} {(b - f)}^{1} (b + f))$

Step 6.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 ({(b - f)}^{1 + 1} (b + f))$

Step 6.1.4

Add $1$ and $1$ .

$3 ({(b - f)}^{2} (b + f))$

Step 6.2

Remove unnecessary parentheses.

$3 {(b - f)}^{2} (b + f)$