Solve (-1/4ax^{2}-5/2ax^{2}+1/3ax^{2})*(-2a^2+3/2a^2+frac{1}{2}a^2+a^2)

$$( - \frac { 1 } { 4 } a x ^ { 2 } - \frac { 5 } { 2 } a x ^ { 2 } + \frac { 1 } { 3 } a x ^ { 2 } ) \cdot ( - 2 a ^ { 2 } + \frac { 3 } { 2 } a ^ { 2 } + \frac { 1 } { 2 } a ^ { 2 } + a ^ { 2 } )$$

Evaluate

$$-\frac{29x^{2}a^{3}}{12}$$

Solution Steps

Combine -\frac{1}{4}ax^{2} and -\frac{5}{2}ax^{2} to get -\frac{11}{4}ax^{2}.

$$\left(-\frac{11}{4}ax^{2}+\frac{1}{3}ax^{2}\right)\left(-2a^{2}+\frac{3}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

Combine -\frac{11}{4}ax^{2} and \frac{1}{3}ax^{2} to get -\frac{29}{12}ax^{2}.

$$-\frac{29}{12}ax^{2}\left(-2a^{2}+\frac{3}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

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

$$-\frac{29}{12}ax^{2}\left(-\frac{1}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

Combine -\frac{1}{2}a^{2} and \frac{1}{2}a^{2} to get 0.

$$-\frac{29}{12}ax^{2}a^{2}$$

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

$$-\frac{29}{12}a^{3}x^{2}$$

Expand

$$-\frac{29x^{2}a^{3}}{12}$$

Solution Steps

Combine -\frac{1}{4}ax^{2} and -\frac{5}{2}ax^{2} to get -\frac{11}{4}ax^{2}.

$$\left(-\frac{11}{4}ax^{2}+\frac{1}{3}ax^{2}\right)\left(-2a^{2}+\frac{3}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

Combine -\frac{11}{4}ax^{2} and \frac{1}{3}ax^{2} to get -\frac{29}{12}ax^{2}.

$$-\frac{29}{12}ax^{2}\left(-2a^{2}+\frac{3}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

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

$$-\frac{29}{12}ax^{2}\left(-\frac{1}{2}a^{2}+\frac{1}{2}a^{2}+a^{2}\right)$$

Combine -\frac{1}{2}a^{2} and \frac{1}{2}a^{2} to get 0.

$$-\frac{29}{12}ax^{2}a^{2}$$

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

$$-\frac{29}{12}a^{3}x^{2}$$