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

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

Evaluate

$$3x^{7}-5x^{6}-\frac{5x^{5}}{3}+x^{4}$$

Solution Steps

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

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

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

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

Use the distributive property to multiply \frac{1}{6}x^{3} by -3x^{2}+4x+3.

$$\left(-\frac{1}{2}x^{5}+\frac{2}{3}x^{4}+\frac{1}{2}x^{3}\right)\left(2x-6x^{2}\right)$$

Use the distributive property to multiply -\frac{1}{2}x^{5}+\frac{2}{3}x^{4}+\frac{1}{2}x^{3} by 2x-6x^{2} and combine like terms.

$$-5x^{6}+3x^{7}-\frac{5}{3}x^{5}+x^{4}$$

Expand

$$3x^{7}-5x^{6}-\frac{5x^{5}}{3}+x^{4}$$

Solution Steps

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

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

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

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

Use the distributive property to multiply \frac{1}{6}x^{3} by -3x^{2}+4x+3.

$$\left(-\frac{1}{2}x^{5}+\frac{2}{3}x^{4}+\frac{1}{2}x^{3}\right)\left(2x-6x^{2}\right)$$

Use the distributive property to multiply -\frac{1}{2}x^{5}+\frac{2}{3}x^{4}+\frac{1}{2}x^{3} by 2x-6x^{2} and combine like terms.

$$-5x^{6}+3x^{7}-\frac{5}{3}x^{5}+x^{4}$$