Solve -[-1/2*(2x^{3}+5x^2-3x+0)-3/2*(2x^4+x^3+0x^2+x+0)]

$$- [ - \frac { 1 } { 2 } \cdot ( 2 x ^ { 3 } + 5 x ^ { 2 } - 3 x + 0 ) - \frac { 3 } { 2 } \cdot ( 2 x ^ { 4 } + x ^ { 3 } + 0 x ^ { 2 } + x + 0 ) ]$$

Evaluate

$$\frac{x^{2}\left(6x^{2}+5x+5\right)}{2}$$

Solution Steps

Anything plus zero gives itself.

$$-\left(-\frac{1}{2}\left(2x^{3}+5x^{2}-3x\right)-\frac{3}{2}\left(2x^{4}+x^{3}+0x^{2}+x\right)\right)$$

Use the distributive property to multiply -\frac{1}{2} by 2x^{3}+5x^{2}-3x.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-\frac{3}{2}\left(2x^{4}+x^{3}+0x^{2}+x\right)\right)$$

Anything times zero gives zero.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-\frac{3}{2}\left(2x^{4}+x^{3}+x\right)\right)$$

Use the distributive property to multiply -\frac{3}{2} by 2x^{4}+x^{3}+x.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-3x^{4}-\frac{3}{2}x^{3}-\frac{3}{2}x\right)$$

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

$$-\left(-\frac{5}{2}x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-3x^{4}-\frac{3}{2}x\right)$$

Combine \frac{3}{2}x and -\frac{3}{2}x to get 0.

$$-\left(-\frac{5}{2}x^{3}-\frac{5}{2}x^{2}-3x^{4}\right)$$

To find the opposite of -\frac{5}{2}x^{3}-\frac{5}{2}x^{2}-3x^{4}, find the opposite of each term.

$$\frac{5}{2}x^{3}+\frac{5}{2}x^{2}+3x^{4}$$

Expand

$$3x^{4}+\frac{5x^{3}}{2}+\frac{5x^{2}}{2}$$

Solution Steps

Anything plus zero gives itself.

$$-\left(-\frac{1}{2}\left(2x^{3}+5x^{2}-3x\right)-\frac{3}{2}\left(2x^{4}+x^{3}+0x^{2}+x\right)\right)$$

Use the distributive property to multiply -\frac{1}{2} by 2x^{3}+5x^{2}-3x.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-\frac{3}{2}\left(2x^{4}+x^{3}+0x^{2}+x\right)\right)$$

Anything times zero gives zero.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-\frac{3}{2}\left(2x^{4}+x^{3}+x\right)\right)$$

Use the distributive property to multiply -\frac{3}{2} by 2x^{4}+x^{3}+x.

$$-\left(-x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-3x^{4}-\frac{3}{2}x^{3}-\frac{3}{2}x\right)$$

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

$$-\left(-\frac{5}{2}x^{3}-\frac{5}{2}x^{2}+\frac{3}{2}x-3x^{4}-\frac{3}{2}x\right)$$

Combine \frac{3}{2}x and -\frac{3}{2}x to get 0.

$$-\left(-\frac{5}{2}x^{3}-\frac{5}{2}x^{2}-3x^{4}\right)$$

To find the opposite of -\frac{5}{2}x^{3}-\frac{5}{2}x^{2}-3x^{4}, find the opposite of each term.

$$\frac{5}{2}x^{3}+\frac{5}{2}x^{2}+3x^{4}$$