Factor 224m^3+32m^2-56m-8

$224 m^{3} + 32 m^{2} - 56 m - 8$

Factor $8$ out of $224 m^{3} + 32 m^{2} - 56 m - 8$ .

Factor $8$ out of $224 m^{3}$ .

$8 (28 m^{3}) + 32 m^{2} - 56 m - 8$

Factor $8$ out of $32 m^{2}$ .

$8 (28 m^{3}) + 8 (4 m^{2}) - 56 m - 8$

Factor $8$ out of $- 56 m$ .

$8 (28 m^{3}) + 8 (4 m^{2}) + 8 (- 7 m) - 8$

Factor $8$ out of $- 8$ .

$8 (28 m^{3}) + 8 (4 m^{2}) + 8 (- 7 m) + 8 (- 1)$

Factor $8$ out of $8 (28 m^{3}) + 8 (4 m^{2})$ .

$8 (28 m^{3} + 4 m^{2}) + 8 (- 7 m) + 8 (- 1)$

Factor $8$ out of $8 (28 m^{3} + 4 m^{2}) + 8 (- 7 m)$ .

$8 (28 m^{3} + 4 m^{2} - 7 m) + 8 (- 1)$

Factor $8$ out of $8 (28 m^{3} + 4 m^{2} - 7 m) + 8 (- 1)$ .

$8 (28 m^{3} + 4 m^{2} - 7 m - 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$8 ((28 m^{3} + 4 m^{2}) - 7 m - 1)$

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

$8 (4 m^{2} (7 m + 1) - (7 m + 1))$

Factor the polynomial by factoring out the greatest common factor, $7 m + 1$ .

$8 ((7 m + 1) (4 m^{2} - 1))$

Rewrite $4 m^{2}$ as ${(2 m)}^{2}$ .

$8 ((7 m + 1) ({(2 m)}^{2} - 1))$

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

$8 ((7 m + 1) ({(2 m)}^{2} - 1^{2}))$

Factor.

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

$8 ((7 m + 1) ((2 m + 1) (2 m - 1)))$

Remove unnecessary parentheses.

$8 ((7 m + 1) (2 m + 1) (2 m - 1))$

Remove unnecessary parentheses.

$8 (7 m + 1) (2 m + 1) (2 m - 1)$