Algebra Examples

$15 a^{3} + 10 a^{2} - 18 b - 27 a b$

Step 1

Regroup terms.

$15 a^{3} - 27 a b + 10 a^{2} - 18 b$

Step 2

Factor $3 a$ out of $15 a^{3} - 27 a b$ .

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Step 2.1

Factor $3 a$ out of $15 a^{3}$ .

$3 a (5 a^{2}) - 27 a b + 10 a^{2} - 18 b$

Step 2.2

Factor $3 a$ out of $- 27 a b$ .

$3 a (5 a^{2}) + 3 a (- 9 b) + 10 a^{2} - 18 b$

Step 2.3

Factor $3 a$ out of $3 a (5 a^{2}) + 3 a (- 9 b)$ .

$3 a (5 a^{2} - 9 b) + 10 a^{2} - 18 b$

Step 3

Factor $2$ out of $10 a^{2} - 18 b$ .

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Step 3.1

Factor $2$ out of $10 a^{2}$ .

$3 a (5 a^{2} - 9 b) + 2 (5 a^{2}) - 18 b$

Step 3.2

Factor $2$ out of $- 18 b$ .

$3 a (5 a^{2} - 9 b) + 2 (5 a^{2}) + 2 (- 9 b)$

Step 3.3

Factor $2$ out of $2 (5 a^{2}) + 2 (- 9 b)$ .

$3 a (5 a^{2} - 9 b) + 2 (5 a^{2} - 9 b)$

Step 4

Factor $5 a^{2} - 9 b$ out of $3 a (5 a^{2} - 9 b) + 2 (5 a^{2} - 9 b)$ .

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Step 4.1

Factor $5 a^{2} - 9 b$ out of $3 a (5 a^{2} - 9 b)$ .

$(5 a^{2} - 9 b) (3 a) + 2 (5 a^{2} - 9 b)$

Step 4.2

Factor $5 a^{2} - 9 b$ out of $2 (5 a^{2} - 9 b)$ .

$(5 a^{2} - 9 b) (3 a) + (5 a^{2} - 9 b) \cdot 2$

Step 4.3

Factor $5 a^{2} - 9 b$ out of $(5 a^{2} - 9 b) (3 a) + (5 a^{2} - 9 b) \cdot 2$ .

$(5 a^{2} - 9 b) (3 a + 2)$