Solve 1/2x(-3x^2+4x+3)-1/3x^2(2x-6x^2)

$$\frac { 1 } { 2 } x ( - 3 x ^ { 2 } + 4 x + 3 ) - \frac { 1 } { 3 } x ^ { 2 } ( 2 x - 6 x ^ { 2 } )$$

Evaluate

$$2x^{4}-\frac{13x^{3}}{6}+2x^{2}+\frac{3x}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}x by -3x^{2}+4x+3.

$$-\frac{3}{2}x^{3}+2x^{2}+\frac{3}{2}x-\frac{1}{3}x^{2}\left(2x-6x^{2}\right)$$

Use the distributive property to multiply -\frac{1}{3}x^{2} by 2x-6x^{2}.

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

Combine -\frac{3}{2}x^{3} and -\frac{2}{3}x^{3} to get -\frac{13}{6}x^{3}.

$$-\frac{13}{6}x^{3}+2x^{2}+\frac{3}{2}x+2x^{4}$$

Expand

$$2x^{4}-\frac{13x^{3}}{6}+2x^{2}+\frac{3x}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}x by -3x^{2}+4x+3.

$$-\frac{3}{2}x^{3}+2x^{2}+\frac{3}{2}x-\frac{1}{3}x^{2}\left(2x-6x^{2}\right)$$

Use the distributive property to multiply -\frac{1}{3}x^{2} by 2x-6x^{2}.

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

Combine -\frac{3}{2}x^{3} and -\frac{2}{3}x^{3} to get -\frac{13}{6}x^{3}.

$$-\frac{13}{6}x^{3}+2x^{2}+\frac{3}{2}x+2x^{4}$$