Solve -7/5ab(-3/14ab)-1/25a^{2}(15/2b^2)+(-frac{6}{5}a^2b+frac{7}{10}a^2b)(-frac{3}{2}a^2b)

$$- \frac { 7 } { 5 } a b ( - \frac { 3 } { 14 } a b ) - \frac { 1 } { 25 } a ^ { 2 } ( \frac { 15 } { 2 } b ^ { 2 } ) + ( - \frac { 6 } { 5 } a ^ { 2 } b + \frac { 7 } { 10 } a ^ { 2 } b ) ( - \frac { 3 } { 2 } a ^ { 2 } b )$$

Evaluate

$$\frac{3b^{2}a^{4}}{4}$$

Solution Steps

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

$$-\frac{7}{5}a^{2}b\left(-\frac{3}{14}\right)b-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

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

$$-\frac{7}{5}a^{2}b^{2}\left(-\frac{3}{14}\right)-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Multiply -\frac{7}{5} and -\frac{3}{14} to get \frac{3}{10}.

$$\frac{3}{10}a^{2}b^{2}-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Multiply \frac{1}{25} and \frac{15}{2} to get \frac{3}{10}.

$$\frac{3}{10}a^{2}b^{2}-\frac{3}{10}a^{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Combine \frac{3}{10}a^{2}b^{2} and -\frac{3}{10}a^{2}b^{2} to get 0.

$$0+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Combine -\frac{6}{5}a^{2}b and \frac{7}{10}a^{2}b to get -\frac{1}{2}a^{2}b.

$$0-\frac{1}{2}a^{2}b\left(-\frac{3}{2}\right)a^{2}b$$

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

$$0+\frac{3}{4}a^{2}ba^{2}b$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$0+\frac{3}{4}a^{4}bb$$

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

$$0+\frac{3}{4}a^{4}b^{2}$$

Anything plus zero gives itself.

$$\frac{3}{4}a^{4}b^{2}$$

Expand

$$\frac{3b^{2}a^{4}}{4}$$

Solution Steps

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

$$-\frac{7}{5}a^{2}b\left(-\frac{3}{14}\right)b-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

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

$$-\frac{7}{5}a^{2}b^{2}\left(-\frac{3}{14}\right)-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Multiply -\frac{7}{5} and -\frac{3}{14} to get \frac{3}{10}.

$$\frac{3}{10}a^{2}b^{2}-\frac{1}{25}a^{2}\times \frac{15}{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Multiply \frac{1}{25} and \frac{15}{2} to get \frac{3}{10}.

$$\frac{3}{10}a^{2}b^{2}-\frac{3}{10}a^{2}b^{2}+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Combine \frac{3}{10}a^{2}b^{2} and -\frac{3}{10}a^{2}b^{2} to get 0.

$$0+\left(-\frac{6}{5}a^{2}b+\frac{7}{10}a^{2}b\right)\left(-\frac{3}{2}\right)a^{2}b$$

Combine -\frac{6}{5}a^{2}b and \frac{7}{10}a^{2}b to get -\frac{1}{2}a^{2}b.

$$0-\frac{1}{2}a^{2}b\left(-\frac{3}{2}\right)a^{2}b$$

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

$$0+\frac{3}{4}a^{2}ba^{2}b$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$0+\frac{3}{4}a^{4}bb$$

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

$$0+\frac{3}{4}a^{4}b^{2}$$

Anything plus zero gives itself.

$$\frac{3}{4}a^{4}b^{2}$$