Factor t^6+t^5-t^4-t^3

$t^{6} + t^{5} - t^{4} - t^{3}$

Factor $t^{3}$ out of $t^{6} + t^{5} - t^{4} - t^{3}$ .

Factor $t^{3}$ out of $t^{6}$ .

$t^{3} t^{3} + t^{5} - t^{4} - t^{3}$

Factor $t^{3}$ out of $t^{5}$ .

$t^{3} t^{3} + t^{3} t^{2} - t^{4} - t^{3}$

Factor $t^{3}$ out of $- t^{4}$ .

$t^{3} t^{3} + t^{3} t^{2} + t^{3} (- t) - t^{3}$

Factor $t^{3}$ out of $- t^{3}$ .

$t^{3} t^{3} + t^{3} t^{2} + t^{3} (- t) + t^{3} \cdot - 1$

Factor $t^{3}$ out of $t^{3} t^{3} + t^{3} t^{2}$ .

$t^{3} (t^{3} + t^{2}) + t^{3} (- t) + t^{3} \cdot - 1$

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

$t^{3} (t^{3} + t^{2} - t) + t^{3} \cdot - 1$

Factor $t^{3}$ out of $t^{3} (t^{3} + t^{2} - t) + t^{3} \cdot - 1$ .

$t^{3} (t^{3} + t^{2} - t - 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$t^{3} ((t^{3} + t^{2}) - t - 1)$

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

$t^{3} (t^{2} (t + 1) - (t + 1))$

Factor the polynomial by factoring out the greatest common factor, $t + 1$ .

$t^{3} ((t + 1) (t^{2} - 1))$

Rewrite $1$ as $1^{2}$ .

$t^{3} ((t + 1) (t^{2} - 1^{2}))$

Factor.

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

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

Remove unnecessary parentheses.

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

Factor.

Combine exponents.

Raise $t + 1$ to the power of $1$ .

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

Raise $t + 1$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

$t^{3} ({(t + 1)}^{2} (t - 1))$

Remove unnecessary parentheses.

$t^{3} {(t + 1)}^{2} (t - 1)$