Solve 3x-{x^{4}-2[x^3-3x^4+2(x^4-x)+x^4]+2x}

$$3 x - \{ x ^ { 4 } - 2 [ x ^ { 3 } - 3 x ^ { 4 } + 2 ( x ^ { 4 } - x ) + x ^ { 4 } ] + 2 x \}$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 2 by x^{4}-x.

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

Combine -3x^{4} and 2x^{4} to get -x^{4}.

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

Combine -x^{4} and x^{4} to get 0.

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

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

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

Combine 4x and 2x to get 6x.

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

To find the opposite of x^{4}-2x^{3}+6x, find the opposite of each term.

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

Combine 3x and -6x to get -3x.

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

Expand

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

Solution Steps

Use the distributive property to multiply 2 by x^{4}-x.

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

Combine -3x^{4} and 2x^{4} to get -x^{4}.

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

Combine -x^{4} and x^{4} to get 0.

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

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

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

Combine 4x and 2x to get 6x.

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

To find the opposite of x^{4}-2x^{3}+6x, find the opposite of each term.

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

Combine 3x and -6x to get -3x.

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