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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply 2x by x^{2}+1.

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

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

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

Use the distributive property to multiply -4x by x-3.

$$2x^{3}+2x-4x^{2}+12x+2x^{2}-6x+2$$

Combine 2x and 12x to get 14x.

$$2x^{3}+14x-4x^{2}+2x^{2}-6x+2$$

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

$$2x^{3}+14x-2x^{2}-6x+2$$

Combine 14x and -6x to get 8x.

$$2x^{3}+8x-2x^{2}+2$$

Expand

$$2x^{3}-2x^{2}+8x+2$$

Solution Steps

Use the distributive property to multiply 2x by x^{2}+1.

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

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

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

Use the distributive property to multiply -4x by x-3.

$$2x^{3}+2x-4x^{2}+12x+2x^{2}-6x+2$$

Combine 2x and 12x to get 14x.

$$2x^{3}+14x-4x^{2}+2x^{2}-6x+2$$

Combine -4x^{2} and 2x^{2} to get -2x^{2}.

$$2x^{3}+14x-2x^{2}-6x+2$$

Combine 14x and -6x to get 8x.

$$2x^{3}+8x-2x^{2}+2$$