Solve -5/4a^2-3/2ab+1/2a^2+5ab-3a^2-1/2ab

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

Evaluate

$$\frac{3a\left(4b-5a\right)}{4}$$

Solution Steps

Combine -\frac{5}{4}a^{2} and \frac{1}{2}a^{2} to get -\frac{3}{4}a^{2}.

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

Combine -\frac{3}{2}ab and 5ab to get \frac{7}{2}ab.

$$-\frac{3}{4}a^{2}+\frac{7}{2}ab-3a^{2}-\frac{1}{2}ab$$

Combine -\frac{3}{4}a^{2} and -3a^{2} to get -\frac{15}{4}a^{2}.

$$-\frac{15}{4}a^{2}+\frac{7}{2}ab-\frac{1}{2}ab$$

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

$$-\frac{15}{4}a^{2}+3ab$$

Factor

$$\frac{3a\left(4b-5a\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-5a^{2}-6ab+2a^{2}+20ab-12a^{2}-2ab}{4}$$

Consider -5a^{2}-6ab+2a^{2}+20ab-12a^{2}-2ab. Factor out a.

$$a\left(-5a-6b+2a+20b-12a-2b\right)$$

Consider -5a-6b+2a+20b-12a-2b. Multiply and combine like terms.

$$-15a+12b$$

Consider -15a+12b. Factor out 3.

$$3\left(-5a+4b\right)$$

Rewrite the complete factored expression.

$$\frac{3a\left(-5a+4b\right)}{4}$$