Solve (7x^{4}-6x^2+x)-(10x^3+2x^2+4x)+(x^2-x)

$$( 7 x ^ { 4 } - 6 x ^ { 2 } + x ) - ( 10 x ^ { 3 } + 2 x ^ { 2 } + 4 x ) + ( x ^ { 2 } - x )$$

Evaluate

$$x\left(7x^{3}-10x^{2}-7x-4\right)$$

Solution Steps

To find the opposite of 10x^{3}+2x^{2}+4x, find the opposite of each term.

$$7x^{4}-6x^{2}+x-10x^{3}-2x^{2}-4x+x^{2}-x$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

$$7x^{4}-8x^{2}+x-10x^{3}-4x+x^{2}-x$$

Combine x and -4x to get -3x.

$$7x^{4}-8x^{2}-3x-10x^{3}+x^{2}-x$$

Combine -8x^{2} and x^{2} to get -7x^{2}.

$$7x^{4}-7x^{2}-3x-10x^{3}-x$$

Combine -3x and -x to get -4x.

$$7x^{4}-7x^{2}-4x-10x^{3}$$

Expand

$$7x^{4}-10x^{3}-7x^{2}-4x$$

Solution Steps

To find the opposite of 10x^{3}+2x^{2}+4x, find the opposite of each term.

$$7x^{4}-6x^{2}+x-10x^{3}-2x^{2}-4x+x^{2}-x$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

$$7x^{4}-8x^{2}+x-10x^{3}-4x+x^{2}-x$$

Combine x and -4x to get -3x.

$$7x^{4}-8x^{2}-3x-10x^{3}+x^{2}-x$$

Combine -8x^{2} and x^{2} to get -7x^{2}.

$$7x^{4}-7x^{2}-3x-10x^{3}-x$$

Combine -3x and -x to get -4x.

$$7x^{4}-7x^{2}-4x-10x^{3}$$