Solve [2x*(-x^2)+3x+2x^3]+(2x-6x^2)-(3x+3x^2

$$[ 2 x \cdot ( - x ^ { 2 } ) + 3 x + 2 x ^ { 3 } ] + ( 2 x - 6 x ^ { 2 } ) - ( 3 x + 3 x ^ { 2 }$$

Evaluate

$$x\left(2-9x\right)$$

Solution Steps

Combine 3x and 2x to get 5x.

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

To find the opposite of 3x+3x^{2}, find the opposite of each term.

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

Combine 5x and -3x to get 2x.

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

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

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

Multiply 2 and -1 to get -2.

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

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

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

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

$$2x-9x^{2}$$

Expand

$$2x-9x^{2}$$

Solution Steps

Combine 3x and 2x to get 5x.

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

To find the opposite of 3x+3x^{2}, find the opposite of each term.

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

Combine 5x and -3x to get 2x.

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

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

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

Multiply 2 and -1 to get -2.

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

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

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

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

$$2x-9x^{2}$$