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4x^{5}+2x^{3}+8x^{2}+4-\left(x^{2}+x+1\right)
Use the distributive property to multiply x^{3}+2 by 4x^{2}+2.
4x^{5}+2x^{3}+8x^{2}+4-x^{2}-x-1
To find the opposite of x^{2}+x+1, find the opposite of each term.
4x^{5}+2x^{3}+7x^{2}+4-x-1
Combine 8x^{2} and -x^{2} to get 7x^{2}.
4x^{5}+2x^{3}+7x^{2}+3-x
Subtract 1 from 4 to get 3.
4x^{5}+2x^{3}+8x^{2}+4-\left(x^{2}+x+1\right)
Use the distributive property to multiply x^{3}+2 by 4x^{2}+2.
4x^{5}+2x^{3}+8x^{2}+4-x^{2}-x-1
To find the opposite of x^{2}+x+1, find the opposite of each term.
4x^{5}+2x^{3}+7x^{2}+4-x-1
Combine 8x^{2} and -x^{2} to get 7x^{2}.
4x^{5}+2x^{3}+7x^{2}+3-x
Subtract 1 from 4 to get 3.