Solve (u^2-5u+1)(-u+1)

$$( u ^ { 2 } - 5 u + 1 ) ( - u + 1 )$$

Evaluate

$$\left(1-u\right)\left(u^{2}-5u+1\right)$$

Solution Steps

Use the distributive property to multiply u^{2}-5u+1 by -u+1.

$$u^{2}\left(-u\right)+u^{2}-5u\left(-u\right)-5u-u+1$$

Multiply -5 and -1 to get 5.

$$u^{2}\left(-u\right)+u^{2}+5uu-5u-u+1$$

Multiply u and u to get u^{2}.

$$u^{2}\left(-u\right)+u^{2}+5u^{2}-5u-u+1$$

Combine u^{2} and 5u^{2} to get 6u^{2}.

$$u^{2}\left(-u\right)+6u^{2}-5u-u+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$u^{3}\left(-1\right)+6u^{2}-5u-u+1$$

Combine -5u and -u to get -6u.

$$u^{3}\left(-1\right)+6u^{2}-6u+1$$

Expand

$$1-6u+6u^{2}-u^{3}$$

Solution Steps

Use the distributive property to multiply u^{2}-5u+1 by -u+1.

$$u^{2}\left(-u\right)+u^{2}-5u\left(-u\right)-5u-u+1$$

Multiply -5 and -1 to get 5.

$$u^{2}\left(-u\right)+u^{2}+5uu-5u-u+1$$

Multiply u and u to get u^{2}.

$$u^{2}\left(-u\right)+u^{2}+5u^{2}-5u-u+1$$

Combine u^{2} and 5u^{2} to get 6u^{2}.

$$u^{2}\left(-u\right)+6u^{2}-5u-u+1$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$u^{3}\left(-1\right)+6u^{2}-5u-u+1$$

Combine -5u and -u to get -6u.

$$u^{3}\left(-1\right)+6u^{2}-6u+1$$