Solve (3x)(2x^5)-2x^3(6x^2)/6x^4

$$\frac { ( 3 x ) ( 2 x ^ { 5 } ) - 2 x ^ { 3 } ( 6 x ^ { 2 } ) } { 6 x ^ { 4 } }$$

Evaluate

$$x\left(x-2\right)$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3x^{6}\times 2-2x^{5}\times 6}{6x^{4}}$$

Multiply 3 and 2 to get 6.

$$\frac{6x^{6}-2x^{5}\times 6}{6x^{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{6x^{6}-12x^{5}}{6x^{4}}$$

Factor the expressions that are not already factored.

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

Cancel out 6x^{4} in both numerator and denominator.

$$x\left(x-2\right)$$

Expand the expression.

$$x^{2}-2x$$

Expand

$$x^{2}-2x$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3x^{6}\times 2-2x^{5}\times 6}{6x^{4}}$$

Multiply 3 and 2 to get 6.

$$\frac{6x^{6}-2x^{5}\times 6}{6x^{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{6x^{6}-12x^{5}}{6x^{4}}$$

Factor the expressions that are not already factored.

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

Cancel out 6x^{4} in both numerator and denominator.

$$x\left(x-2\right)$$

Expand the expression.

$$x^{2}-2x$$