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

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

Evaluate

$$2+x^{2}+x^{3}+x^{5}-x^{6}$$

Solution Steps

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

$$\left(-x^{3}\right)x^{3}-x^{3}+x^{5}+x^{2}+2x^{3}+2$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-x^{6}-x^{3}+x^{5}+x^{2}+2x^{3}+2$$

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

$$-x^{6}+x^{3}+x^{5}+x^{2}+2$$

Expand

$$2+x^{2}+x^{3}+x^{5}-x^{6}$$

Solution Steps

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

$$\left(-x^{3}\right)x^{3}-x^{3}+x^{5}+x^{2}+2x^{3}+2$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-x^{6}-x^{3}+x^{5}+x^{2}+2x^{3}+2$$

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

$$-x^{6}+x^{3}+x^{5}+x^{2}+2$$