Solve (4ab-5a^2-2a)+(-18a^2-14ab-1/3a)+(-10ab-20a^2-7/3a)

$$( 4 a b - 5 a ^ { 2 } - 2 a ) + ( - 18 a ^ { 2 } - 14 a b - \frac { 1 } { 3 } a ) + ( - 10 a b - 20 a ^ { 2 } - \frac { 7 } { 3 } a )$$

Evaluate

$$-\frac{a\left(129a+60b+14\right)}{3}$$

Solution Steps

Combine -5a^{2} and -18a^{2} to get -23a^{2}.

$$4ab-23a^{2}-2a-14ab-\frac{1}{3}a-10ab-20a^{2}-\frac{7}{3}a$$

Combine 4ab and -14ab to get -10ab.

$$-10ab-23a^{2}-2a-\frac{1}{3}a-10ab-20a^{2}-\frac{7}{3}a$$

Combine -2a and -\frac{1}{3}a to get -\frac{7}{3}a.

$$-10ab-23a^{2}-\frac{7}{3}a-10ab-20a^{2}-\frac{7}{3}a$$

Combine -10ab and -10ab to get -20ab.

$$-20ab-23a^{2}-\frac{7}{3}a-20a^{2}-\frac{7}{3}a$$

Combine -23a^{2} and -20a^{2} to get -43a^{2}.

$$-20ab-43a^{2}-\frac{7}{3}a-\frac{7}{3}a$$

Combine -\frac{7}{3}a and -\frac{7}{3}a to get -\frac{14}{3}a.

$$-20ab-43a^{2}-\frac{14}{3}a$$

Factor

$$-\frac{a\left(129a+60b+14\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{12ab-15a^{2}-6a-54a^{2}-42ab-a-30ab-60a^{2}-7a}{3}$$

Consider 12ab-15a^{2}-6a-54a^{2}-42ab-a-30ab-60a^{2}-7a. Factor out a.

$$a\left(-60b-129a-14\right)$$

Consider 12b-15a-6-54a-42b-1-30b-60a-7. Multiply and combine like terms.

$$-129a-60b-14$$

Rewrite the complete factored expression.

$$\frac{a\left(-129a-60b-14\right)}{3}$$