Solve 1-m^3(-m^2-m-1)

$$1 - m ^ { 3 } ( - m ^ { 2 } - m - 1 )$$

Evaluate

$$m^{5}+m^{4}+m^{3}+1$$

Solution Steps

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

$$1-\left(m^{3}\left(-m^{2}\right)-m^{4}-m^{3}\right)$$

To find the opposite of m^{3}\left(-m^{2}\right)-m^{4}-m^{3}, find the opposite of each term.

$$1-m^{3}\left(-m^{2}\right)+m^{4}+m^{3}$$

Multiply -1 and -1 to get 1.

$$1+m^{3}m^{2}+m^{4}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$1+m^{5}+m^{4}+m^{3}$$

Expand

$$m^{5}+m^{4}+m^{3}+1$$

Solution Steps

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

$$1-\left(m^{3}\left(-m^{2}\right)-m^{4}-m^{3}\right)$$

To find the opposite of m^{3}\left(-m^{2}\right)-m^{4}-m^{3}, find the opposite of each term.

$$1-m^{3}\left(-m^{2}\right)+m^{4}+m^{3}$$

Multiply -1 and -1 to get 1.

$$1+m^{3}m^{2}+m^{4}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$1+m^{5}+m^{4}+m^{3}$$