Solve 2/7ab-1/4b^2+3/2b+3/14ab-frac{1}{5}b^2

$$\frac{ 2 }{ 7 } ab- \frac{ 1 }{ 4 } { b }^{ 2 } + \frac{ 3 }{ 2 } b+ \frac{ 3 }{ 14 } ab- \frac{ 1 }{ 5 } { b }^{ 2 }$$

Evaluate

$$\frac{b\left(10a-9b+30\right)}{20}$$

Solution Steps

Combine \frac{2}{7}ab and \frac{3}{14}ab to get \frac{1}{2}ab.

$$\frac{1}{2}ab-\frac{1}{4}b^{2}+\frac{3}{2}b-\frac{1}{5}b^{2}$$

Combine -\frac{1}{4}b^{2} and -\frac{1}{5}b^{2} to get -\frac{9}{20}b^{2}.

$$\frac{1}{2}ab-\frac{9}{20}b^{2}+\frac{3}{2}b$$

Factor

$$\frac{b\left(10a-9b+30\right)}{20}$$

Solution Steps

Factor out \frac{1}{140}.

$$\frac{40ab-35b^{2}+210b+30ab-28b^{2}}{140}$$

Consider 40ab-35b^{2}+210b+30ab-28b^{2}. Factor out b.

$$b\left(40a-35b+210+30a-28b\right)$$

Consider 40a-35b+210+30a-28b. Multiply and combine like terms.

$$70a-63b+210$$

Consider 70a-63b+210. Factor out 7.

$$7\left(10a-9b+30\right)$$

Rewrite the complete factored expression.

$$\frac{b\left(10a-9b+30\right)}{20}$$