Solve k(k+1)(k+2)(k+3)+4(k+1)(k+2)(k+3)

$$k ( k + 1 ) ( k + 2 ) ( k + 3 ) + 4 ( k + 1 ) ( k + 2 ) ( k + 3 )$$

Evaluate

$$\left(k+1\right)\left(k+2\right)\left(k+3\right)\left(k+4\right)$$

Solution Steps

Use the distributive property to multiply k by k+1.

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

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

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

Combine 2k^{2} and k^{2} to get 3k^{2}.

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

Apply the distributive property by multiplying each term of k^{3}+3k^{2}+2k by each term of k+3.

$$k^{4}+3k^{3}+3k^{3}+9k^{2}+2k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Combine 3k^{3} and 3k^{3} to get 6k^{3}.

$$k^{4}+6k^{3}+9k^{2}+2k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Combine 9k^{2} and 2k^{2} to get 11k^{2}.

$$k^{4}+6k^{3}+11k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Use the distributive property to multiply 4 by k+1.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k+4\right)\left(k+2\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of 4k+4 by each term of k+2.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k^{2}+8k+4k+8\right)\left(k+3\right)$$

Combine 8k and 4k to get 12k.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k^{2}+12k+8\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of 4k^{2}+12k+8 by each term of k+3.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+12k^{2}+12k^{2}+36k+8k+24$$

Combine 12k^{2} and 12k^{2} to get 24k^{2}.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+24k^{2}+36k+8k+24$$

Combine 36k and 8k to get 44k.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+24k^{2}+44k+24$$

Combine 6k^{3} and 4k^{3} to get 10k^{3}.

$$k^{4}+10k^{3}+11k^{2}+6k+24k^{2}+44k+24$$

Combine 11k^{2} and 24k^{2} to get 35k^{2}.

$$k^{4}+10k^{3}+35k^{2}+6k+44k+24$$

Combine 6k and 44k to get 50k.

$$k^{4}+10k^{3}+35k^{2}+50k+24$$

Expand

$$k^{4}+10k^{3}+35k^{2}+50k+24$$

Solution Steps

Use the distributive property to multiply k by k+1.

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

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

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

Combine 2k^{2} and k^{2} to get 3k^{2}.

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

Apply the distributive property by multiplying each term of k^{3}+3k^{2}+2k by each term of k+3.

$$k^{4}+3k^{3}+3k^{3}+9k^{2}+2k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Combine 3k^{3} and 3k^{3} to get 6k^{3}.

$$k^{4}+6k^{3}+9k^{2}+2k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Combine 9k^{2} and 2k^{2} to get 11k^{2}.

$$k^{4}+6k^{3}+11k^{2}+6k+4\left(k+1\right)\left(k+2\right)\left(k+3\right)$$

Use the distributive property to multiply 4 by k+1.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k+4\right)\left(k+2\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of 4k+4 by each term of k+2.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k^{2}+8k+4k+8\right)\left(k+3\right)$$

Combine 8k and 4k to get 12k.

$$k^{4}+6k^{3}+11k^{2}+6k+\left(4k^{2}+12k+8\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of 4k^{2}+12k+8 by each term of k+3.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+12k^{2}+12k^{2}+36k+8k+24$$

Combine 12k^{2} and 12k^{2} to get 24k^{2}.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+24k^{2}+36k+8k+24$$

Combine 36k and 8k to get 44k.

$$k^{4}+6k^{3}+11k^{2}+6k+4k^{3}+24k^{2}+44k+24$$

Combine 6k^{3} and 4k^{3} to get 10k^{3}.

$$k^{4}+10k^{3}+11k^{2}+6k+24k^{2}+44k+24$$

Combine 11k^{2} and 24k^{2} to get 35k^{2}.

$$k^{4}+10k^{3}+35k^{2}+6k+44k+24$$

Combine 6k and 44k to get 50k.

$$k^{4}+10k^{3}+35k^{2}+50k+24$$