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

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

Evaluate

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

Solution Steps

Combine \frac{1}{2}ab and -\frac{3}{4}ab to get -\frac{1}{4}ab.

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

Combine \frac{2}{3}a^{2} and \frac{1}{3}a^{2} to get a^{2}.

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

Factor

$$\frac{20a^{2}-5ab-40b^{2}-12b}{20}$$

Solution Steps

Factor out \frac{1}{60}.

$$\frac{40a^{2}+30ab-120b^{2}-45ab+20a^{2}-36b}{60}$$

Consider 40a^{2}+30ab-120b^{2}-45ab+20a^{2}-36b. Multiply and combine like terms.

$$60a^{2}-15ab-120b^{2}-36b$$

Consider 60a^{2}-15ab-120b^{2}-36b. Factor out 3.

$$3\left(20a^{2}-5ab-40b^{2}-12b\right)$$

Rewrite the complete factored expression.

$$\frac{20a^{2}-5ab-40b^{2}-12b}{20}$$