Pre-Algebra Examples

$r^{3} - 11 r^{2} - 121 r + 1331$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$(r^{3} - 11 r^{2}) - 121 r + 1331$

Step 1.2

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

$r^{2} (r - 11) - 121 (r - 11)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $r - 11$ .

$(r - 11) (r^{2} - 121)$

Step 3

Rewrite $121$ as $11^{2}$ .

$(r - 11) (r^{2} - 11^{2})$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = 11$ .

$(r - 11) ((r + 11) (r - 11))$

Step 4.2

Remove unnecessary parentheses.

$(r - 11) (r + 11) (r - 11)$

Step 5

Combine exponents.

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Step 5.1

Raise $r - 11$ to the power of $1$ .

${(r - 11)}^{1} (r - 11) (r + 11)$

Step 5.2

Raise $r - 11$ to the power of $1$ .

${(r - 11)}^{1} {(r - 11)}^{1} (r + 11)$

Step 5.3

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

${(r - 11)}^{1 + 1} (r + 11)$

Step 5.4

Add $1$ and $1$ .

${(r - 11)}^{2} (r + 11)$