Basic Math Examples

${(t + 1)}^{3} - 49 (t + 1)$

Step 1

Factor $t + 1$ out of ${(t + 1)}^{3} - 49 (t + 1)$ .

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Step 1.1

Factor $t + 1$ out of ${(t + 1)}^{3}$ .

$(t + 1) {(t + 1)}^{2} - 49 (t + 1)$

Step 1.2

Factor $t + 1$ out of $- 49 (t + 1)$ .

$(t + 1) {(t + 1)}^{2} + (t + 1) \cdot - 49$

Step 1.3

Factor $t + 1$ out of $(t + 1) {(t + 1)}^{2} + (t + 1) \cdot - 49$ .

$(t + 1) ({(t + 1)}^{2} - 49)$

Step 2

Rewrite $49$ as $7^{2}$ .

$(t + 1) ({(t + 1)}^{2} - 7^{2})$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = t + 1$ and $b = 7$ .

$(t + 1) ((t + 1 + 7) (t + 1 - 7))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Add $1$ and $7$ .

$(t + 1) ((t + 8) (t + 1 - 7))$

Step 4.1.2

Subtract $7$ from $1$ .

$(t + 1) ((t + 8) (t - 6))$

Step 4.2

Remove unnecessary parentheses.

$(t + 1) (t + 8) (t - 6)$