Factor 21a+24y^3-24y^2-21ay

$21 a + 24 y^{3} - 24 y^{2} - 21 a y$

Step 1

Factor $3$ out of $21 a + 24 y^{3} - 24 y^{2} - 21 a y$ .

Factor $3$ out of $21 a$ .

$3 (7 a) + 24 y^{3} - 24 y^{2} - 21 a y$

Factor $3$ out of $24 y^{3}$ .

$3 (7 a) + 3 (8 y^{3}) - 24 y^{2} - 21 a y$

Factor $3$ out of $- 24 y^{2}$ .

$3 (7 a) + 3 (8 y^{3}) + 3 (- 8 y^{2}) - 21 a y$

Factor $3$ out of $- 21 a y$ .

$3 (7 a) + 3 (8 y^{3}) + 3 (- 8 y^{2}) + 3 (- 7 a y)$

Factor $3$ out of $3 (7 a) + 3 (8 y^{3})$ .

$3 (7 a + 8 y^{3}) + 3 (- 8 y^{2}) + 3 (- 7 a y)$

Factor $3$ out of $3 (7 a + 8 y^{3}) + 3 (- 8 y^{2})$ .

$3 (7 a + 8 y^{3} - 8 y^{2}) + 3 (- 7 a y)$

Factor $3$ out of $3 (7 a + 8 y^{3} - 8 y^{2}) + 3 (- 7 a y)$ .

$3 (7 a + 8 y^{3} - 8 y^{2} - 7 a y)$

Step 2

Regroup terms.

$3 (- 8 y^{2} + 7 a + 8 y^{3} - 7 a y)$

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((- 8 y^{2} + 7 a) + 8 y^{3} - 7 a y)$

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

$3 (1 (- 8 y^{2} + 7 a) - y (- 8 y^{2} + 7 a))$

Step 4

Factor.

Factor the polynomial by factoring out the greatest common factor, $- 8 y^{2} + 7 a$ .

$3 ((- 8 y^{2} + 7 a) (1 - y))$

Remove unnecessary parentheses.

$3 (- 8 y^{2} + 7 a) (1 - y)$

Step 5

Factor.

Factor $- 1$ out of $- 8 y^{2} + 7 a$ .

Factor $- 1$ out of $- 8 y^{2}$ .

$3 (- (8 y^{2}) + 7 a) (1 - y)$

Factor $- 1$ out of $7 a$ .

$3 (- (8 y^{2}) - (- 7 a)) (1 - y)$

Factor $- 1$ out of $- (8 y^{2}) - (- 7 a)$ .

$3 (- (8 y^{2} - 7 a)) (1 - y)$

Remove unnecessary parentheses.

$3 \cdot - 1 (8 y^{2} - 7 a) (1 - y)$

Step 6

Factor.

Combine exponents.

Factor out negative.

$- ((3 (8 y^{2} - 7 a)) (1 - y))$

Multiply $3$ by $- 1$ .

$- 3 ((8 y^{2} - 7 a) (1 - y))$

Remove unnecessary parentheses.

$- 3 (8 y^{2} - 7 a) (1 - y)$

Factor 21a+24y^3-24y^2-21ay

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