Solve [2a^{3}x^{2}+1/2a^{3}x^{2}+(-3/5ax)(+10/3a^2x)-(-4/3ax^2)6a^2](-frac{17}{4}ax^2)

$$[ 2 a ^ { 3 } x ^ { 2 } + \frac { 1 } { 2 } a ^ { 3 } x ^ { 2 } + ( - \frac { 3 } { 5 } a x ) ( + \frac { 10 } { 3 } a ^ { 2 } x ) - ( - \frac { 4 } { 3 } a x ^ { 2 } ) 6 a ^ { 2 } ] ( - \frac { 17 } { 4 } a x ^ { 2 } )$$

Evaluate

$$-\frac{289\left(ax\right)^{4}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x\times \frac{10}{3}x-\left(-\frac{4}{3}ax^{2}\times 6a^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}ax^{2}\times 6a^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(\frac{5}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

Multiply -\frac{3}{5} and \frac{10}{3} to get -2.

$$\left(\frac{5}{2}a^{3}x^{2}-2a^{3}x^{2}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(\frac{1}{2}a^{3}x^{2}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

Multiply -\frac{4}{3} and 6 to get -8.

$$\left(\frac{1}{2}a^{3}x^{2}-\left(-8a^{3}x^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

The opposite of -8a^{3}x^{2} is 8a^{3}x^{2}.

$$\left(\frac{1}{2}a^{3}x^{2}+8a^{3}x^{2}\right)\left(-\frac{17}{4}\right)ax^{2}$$

Combine \frac{1}{2}a^{3}x^{2} and 8a^{3}x^{2} to get \frac{17}{2}a^{3}x^{2}.

$$\frac{17}{2}a^{3}x^{2}\left(-\frac{17}{4}\right)ax^{2}$$

Multiply \frac{17}{2} and -\frac{17}{4} to get -\frac{289}{8}.

$$-\frac{289}{8}a^{3}x^{2}ax^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-\frac{289}{8}a^{4}x^{2}x^{2}$$

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

$$-\frac{289}{8}a^{4}x^{4}$$

Expand

$$-\frac{289\left(ax\right)^{4}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x\times \frac{10}{3}x-\left(-\frac{4}{3}ax^{2}\times 6a^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}ax^{2}\times 6a^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(2a^{3}x^{2}+\frac{1}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(\frac{5}{2}a^{3}x^{2}-\frac{3}{5}a^{3}x^{2}\times \frac{10}{3}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

Multiply -\frac{3}{5} and \frac{10}{3} to get -2.

$$\left(\frac{5}{2}a^{3}x^{2}-2a^{3}x^{2}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

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

$$\left(\frac{1}{2}a^{3}x^{2}-\left(-\frac{4}{3}a^{3}x^{2}\times 6\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

Multiply -\frac{4}{3} and 6 to get -8.

$$\left(\frac{1}{2}a^{3}x^{2}-\left(-8a^{3}x^{2}\right)\right)\left(-\frac{17}{4}\right)ax^{2}$$

The opposite of -8a^{3}x^{2} is 8a^{3}x^{2}.

$$\left(\frac{1}{2}a^{3}x^{2}+8a^{3}x^{2}\right)\left(-\frac{17}{4}\right)ax^{2}$$

Combine \frac{1}{2}a^{3}x^{2} and 8a^{3}x^{2} to get \frac{17}{2}a^{3}x^{2}.

$$\frac{17}{2}a^{3}x^{2}\left(-\frac{17}{4}\right)ax^{2}$$

Multiply \frac{17}{2} and -\frac{17}{4} to get -\frac{289}{8}.

$$-\frac{289}{8}a^{3}x^{2}ax^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-\frac{289}{8}a^{4}x^{2}x^{2}$$

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

$$-\frac{289}{8}a^{4}x^{4}$$