Algebra Examples

$2 a^{2} b - \frac{5}{2} a b^{2} + \frac{7}{12} a b^{2} + \frac{5}{6} a^{2} b$

Step 1

Remove parentheses.

$2 a^{2} b - \frac{5}{2} \cdot a b^{2} + \frac{7}{12} \cdot (a b^{2}) + \frac{5}{6} \cdot (a^{2} b)$

Step 2

Remove parentheses.

$2 a^{2} b - \frac{5}{2} \cdot a b^{2} + \frac{7}{12} \cdot a b^{2} + \frac{5}{6} \cdot (a^{2} b)$

Step 3

Remove parentheses.

$2 a^{2} b - \frac{5}{2} \cdot a b^{2} + \frac{7}{12} \cdot a b^{2} + \frac{5}{6} \cdot a^{2} b$

Step 4

Factor $a b$ out of $2 a^{2} b - \frac{5}{2} \cdot a b^{2} + \frac{7}{12} \cdot a b^{2} + \frac{5}{6} \cdot a^{2} b$ .

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Step 4.1

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

$a b (2 a) - \frac{5}{2} \cdot a b^{2} + \frac{7}{12} \cdot a b^{2} + \frac{5}{6} \cdot a^{2} b$

Step 4.2

Factor $a b$ out of $- \frac{5}{2} \cdot a b^{2}$ .

$a b (2 a) + a b (- \frac{5}{2} b) + \frac{7}{12} \cdot a b^{2} + \frac{5}{6} \cdot a^{2} b$

Step 4.3

Factor $a b$ out of $\frac{7}{12} \cdot a b^{2}$ .

$a b (2 a) + a b (- \frac{5}{2} b) + a b (\frac{7}{12} b) + \frac{5}{6} \cdot a^{2} b$

Step 4.4

Factor $a b$ out of $\frac{5}{6} \cdot a^{2} b$ .

$a b (2 a) + a b (- \frac{5}{2} b) + a b (\frac{7}{12} b) + a b (\frac{5}{6} \cdot a)$

Step 4.5

Factor $a b$ out of $a b (2 a) + a b (- \frac{5}{2} b)$ .

$a b (2 a - \frac{5}{2} b) + a b (\frac{7}{12} b) + a b (\frac{5}{6} \cdot a)$

Step 4.6

Factor $a b$ out of $a b (2 a - \frac{5}{2} b) + a b (\frac{7}{12} b)$ .

$a b (2 a - \frac{5}{2} b + \frac{7}{12} b) + a b (\frac{5}{6} \cdot a)$

Step 4.7

Factor $a b$ out of $a b (2 a - \frac{5}{2} b + \frac{7}{12} b) + a b (\frac{5}{6} \cdot a)$ .

$a b (2 a - \frac{5}{2} b + \frac{7}{12} b + \frac{5}{6} \cdot a)$

Step 5

Combine exponents.

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Step 5.1

Combine $b$ and $\frac{5}{2}$ .

$a b (2 a - \frac{b \cdot 5}{2} + \frac{7}{12} b + \frac{5}{6} \cdot a)$

Step 5.2

Combine $\frac{7}{12}$ and $b$ .

$a b (2 a - \frac{b \cdot 5}{2} + \frac{7 b}{12} + \frac{5}{6} \cdot a)$

Step 5.3

Combine $\frac{5}{6}$ and $a$ .

$a b (2 a - \frac{b \cdot 5}{2} + \frac{7 b}{12} + \frac{5 a}{6})$