Solve -1/4a+b-4a+4/5b-b+7/5b-4a-(-1/5a-b)(+b-5a)=

$$- \frac { 1 } { 4 } a + b - 4 a + \frac { 4 } { 5 } b - b + \frac { 7 } { 5 } b - 4 a - ( - \frac { 1 } { 5 } a - b ) ( + b - 5 a ) =$$

Evaluate

$$-\frac{24ab}{5}+b^{2}-a^{2}+\frac{11b}{5}-\frac{33a}{4}$$

Solution Steps

Combine -\frac{1}{4}a and -4a to get -\frac{17}{4}a.

$$-\frac{17}{4}a+b+\frac{4}{5}b-b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine b and \frac{4}{5}b to get \frac{9}{5}b.

$$-\frac{17}{4}a+\frac{9}{5}b-b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine \frac{9}{5}b and -b to get \frac{4}{5}b.

$$-\frac{17}{4}a+\frac{4}{5}b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine \frac{4}{5}b and \frac{7}{5}b to get \frac{11}{5}b.

$$-\frac{17}{4}a+\frac{11}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine -\frac{17}{4}a and -4a to get -\frac{33}{4}a.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{5}a-b by each term of b-5a.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab-\frac{1}{5}a\left(-5\right)a-b^{2}+5ba\right)$$

Multiply a and a to get a^{2}.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab-\frac{1}{5}a^{2}\left(-5\right)-b^{2}+5ba\right)$$

Express -\frac{1}{5}\left(-5\right) as a single fraction.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+\frac{-\left(-5\right)}{5}a^{2}-b^{2}+5ba\right)$$

Multiply -1 and -5 to get 5.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+\frac{5}{5}a^{2}-b^{2}+5ba\right)$$

Divide 5 by 5 to get 1.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+1a^{2}-b^{2}+5ba\right)$$

Combine -\frac{1}{5}ab and 5ba to get \frac{24}{5}ab.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(\frac{24}{5}ab+1a^{2}-b^{2}\right)$$

To find the opposite of \frac{24}{5}ab+1a^{2}-b^{2}, find the opposite of each term.

$$-\frac{33}{4}a+\frac{11}{5}b-\frac{24}{5}ab-a^{2}-\left(-b^{2}\right)$$

The opposite of -b^{2} is b^{2}.

$$-\frac{33}{4}a+\frac{11}{5}b-\frac{24}{5}ab-a^{2}+b^{2}$$

Expand

$$-\frac{24ab}{5}+b^{2}-a^{2}+\frac{11b}{5}-\frac{33a}{4}$$

Solution Steps

Combine -\frac{1}{4}a and -4a to get -\frac{17}{4}a.

$$-\frac{17}{4}a+b+\frac{4}{5}b-b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine b and \frac{4}{5}b to get \frac{9}{5}b.

$$-\frac{17}{4}a+\frac{9}{5}b-b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine \frac{9}{5}b and -b to get \frac{4}{5}b.

$$-\frac{17}{4}a+\frac{4}{5}b+\frac{7}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine \frac{4}{5}b and \frac{7}{5}b to get \frac{11}{5}b.

$$-\frac{17}{4}a+\frac{11}{5}b-4a-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Combine -\frac{17}{4}a and -4a to get -\frac{33}{4}a.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}a-b\right)\left(b-5a\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{5}a-b by each term of b-5a.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab-\frac{1}{5}a\left(-5\right)a-b^{2}+5ba\right)$$

Multiply a and a to get a^{2}.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab-\frac{1}{5}a^{2}\left(-5\right)-b^{2}+5ba\right)$$

Express -\frac{1}{5}\left(-5\right) as a single fraction.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+\frac{-\left(-5\right)}{5}a^{2}-b^{2}+5ba\right)$$

Multiply -1 and -5 to get 5.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+\frac{5}{5}a^{2}-b^{2}+5ba\right)$$

Divide 5 by 5 to get 1.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(-\frac{1}{5}ab+1a^{2}-b^{2}+5ba\right)$$

Combine -\frac{1}{5}ab and 5ba to get \frac{24}{5}ab.

$$-\frac{33}{4}a+\frac{11}{5}b-\left(\frac{24}{5}ab+1a^{2}-b^{2}\right)$$

To find the opposite of \frac{24}{5}ab+1a^{2}-b^{2}, find the opposite of each term.

$$-\frac{33}{4}a+\frac{11}{5}b-\frac{24}{5}ab-a^{2}-\left(-b^{2}\right)$$

The opposite of -b^{2} is b^{2}.

$$-\frac{33}{4}a+\frac{11}{5}b-\frac{24}{5}ab-a^{2}+b^{2}$$