Solve (k-2)(3-k)(1+k)=

$$( k - 2 ) ( 3 - k ) ( 1 + k ) =$$

Evaluate

$$\left(3-k\right)\left(k-2\right)\left(k+1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of k-2 by each term of 3-k.

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

Combine 3k and 2k to get 5k.

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

Apply the distributive property by multiplying each term of 5k-k^{2}-6 by each term of 1+k.

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

Combine 5k^{2} and -k^{2} to get 4k^{2}.

$$5k+4k^{2}-k^{3}-6-6k$$

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

$$-k+4k^{2}-k^{3}-6$$

Expand

$$-k^{3}+4k^{2}-k-6$$

Solution Steps

Apply the distributive property by multiplying each term of k-2 by each term of 3-k.

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

Combine 3k and 2k to get 5k.

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

Apply the distributive property by multiplying each term of 5k-k^{2}-6 by each term of 1+k.

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

Combine 5k^{2} and -k^{2} to get 4k^{2}.

$$5k+4k^{2}-k^{3}-6-6k$$

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

$$-k+4k^{2}-k^{3}-6$$