Solve (x^3+2)*(4x^2+2)-(x^2+x+1)=T

$$( x ^ { 3 } + 2 ) \cdot ( 4 x ^ { 2 } + 2 ) - ( x ^ { 2 } + x + 1 ) = T$$

Solve for T

$$T=4x^{5}+2x^{3}+7x^{2}-x+3$$

Solution Steps

Use the distributive property to multiply x^{3}+2 by 4x^{2}+2.

$$4x^{5}+2x^{3}+8x^{2}+4-\left(x^{2}+x+1\right)=T$$

To find the opposite of x^{2}+x+1, find the opposite of each term.

$$4x^{5}+2x^{3}+8x^{2}+4-x^{2}-x-1=T$$

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

$$4x^{5}+2x^{3}+7x^{2}+4-x-1=T$$

Subtract 1 from 4 to get 3.

$$4x^{5}+2x^{3}+7x^{2}+3-x=T$$

Swap sides so that all variable terms are on the left hand side.

$$T=4x^{5}+2x^{3}+7x^{2}+3-x$$