Solve (2x)-x*(+2x^2)-3x*(x^2)+2*(3x^3)-9x^2*(-x)=

$$( 2 x ) - x \cdot ( + 2 x ^ { 2 } ) - 3 x \cdot ( x ^ { 2 } ) + 2 \cdot ( 3 x ^ { 3 } ) - 9 x ^ { 2 } \cdot ( - x ) =$$

Evaluate

$$10x^{3}+2x$$

Solution Steps

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

$$2x-x^{3}\times 2-3xx^{2}+2\times 3x^{3}-9x^{2}\left(-x\right)$$

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

$$2x-x^{3}\times 2-3x^{3}+2\times 3x^{3}-9x^{2}\left(-x\right)$$

Multiply 2 and 3 to get 6.

$$2x-x^{3}\times 2-3x^{3}+6x^{3}-9x^{2}\left(-x\right)$$

Combine -3x^{3} and 6x^{3} to get 3x^{3}.

$$2x-x^{3}\times 2+3x^{3}-9x^{2}\left(-x\right)$$

Multiply -1 and 2 to get -2.

$$2x-2x^{3}+3x^{3}-9x^{2}\left(-1\right)x$$

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

$$2x+x^{3}-9x^{2}\left(-1\right)x$$

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

$$2x+x^{3}-9x^{3}\left(-1\right)$$

Multiply -9 and -1 to get 9.

$$2x+x^{3}+9x^{3}$$

Combine x^{3} and 9x^{3} to get 10x^{3}.

$$2x+10x^{3}$$

Factor

$$2x\left(5x^{2}+1\right)$$

Solution Steps

Factor out x.

$$x\left(2-2x^{2}-3x^{2}+6x^{2}+9x^{2}\right)$$

Consider 2-2x^{2}-3x^{2}+6x^{2}+9x^{2}. Multiply and combine like terms.

$$10x^{2}+2$$

Consider 10x^{2}+2. Factor out 2.

$$2\left(5x^{2}+1\right)$$

Rewrite the complete factored expression. Polynomial 5x^{2}+1 is not factored since it does not have any rational roots.

$$2x\left(5x^{2}+1\right)$$