Factor 75a^2c-45a^2d-30bc+18bd

$75 a^{2} c - 45 a^{2} d - 30 b c + 18 b d$

Step 1

Factor $3$ out of $75 a^{2} c - 45 a^{2} d - 30 b c + 18 b d$ .

Factor $3$ out of $75 a^{2} c$ .

$3 (25 a^{2} c) - 45 a^{2} d - 30 b c + 18 b d$

Factor $3$ out of $- 45 a^{2} d$ .

$3 (25 a^{2} c) + 3 (- 15 a^{2} d) - 30 b c + 18 b d$

Factor $3$ out of $- 30 b c$ .

$3 (25 a^{2} c) + 3 (- 15 a^{2} d) + 3 (- 10 b c) + 18 b d$

Factor $3$ out of $18 b d$ .

$3 (25 a^{2} c) + 3 (- 15 a^{2} d) + 3 (- 10 b c) + 3 (6 b d)$

Factor $3$ out of $3 (25 a^{2} c) + 3 (- 15 a^{2} d)$ .

$3 (25 a^{2} c - 15 a^{2} d) + 3 (- 10 b c) + 3 (6 b d)$

Factor $3$ out of $3 (25 a^{2} c - 15 a^{2} d) + 3 (- 10 b c)$ .

$3 (25 a^{2} c - 15 a^{2} d - 10 b c) + 3 (6 b d)$

Factor $3$ out of $3 (25 a^{2} c - 15 a^{2} d - 10 b c) + 3 (6 b d)$ .

$3 (25 a^{2} c - 15 a^{2} d - 10 b c + 6 b d)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((25 a^{2} c - 15 a^{2} d) - 10 b c + 6 b d)$

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

$3 (5 a^{2} (5 c - 3 d) - 2 b (5 c - 3 d))$

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $5 c - 3 d$ .

$3 ((5 c - 3 d) (5 a^{2} - 2 b))$

Remove unnecessary parentheses.

$3 (5 c - 3 d) (5 a^{2} - 2 b)$