Solve (y+1)(y+2)(y+3)(y+4)-120

$$( y + 1 ) ( y + 2 ) ( y + 3 ) ( y + 4 ) - 120$$

Evaluate

$$\left(y-1\right)\left(y+6\right)\left(y^{2}+5y+16\right)$$

Solution Steps

Apply the distributive property by multiplying each term of y+1 by each term of y+2.

$$\left(y^{2}+2y+y+2\right)\left(y+3\right)\left(y+4\right)-120$$

Combine 2y and y to get 3y.

$$\left(y^{2}+3y+2\right)\left(y+3\right)\left(y+4\right)-120$$

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

$$\left(y^{3}+3y^{2}+3y^{2}+9y+2y+6\right)\left(y+4\right)-120$$

Combine 3y^{2} and 3y^{2} to get 6y^{2}.

$$\left(y^{3}+6y^{2}+9y+2y+6\right)\left(y+4\right)-120$$

Combine 9y and 2y to get 11y.

$$\left(y^{3}+6y^{2}+11y+6\right)\left(y+4\right)-120$$

Apply the distributive property by multiplying each term of y^{3}+6y^{2}+11y+6 by each term of y+4.

$$y^{4}+4y^{3}+6y^{3}+24y^{2}+11y^{2}+44y+6y+24-120$$

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

$$y^{4}+10y^{3}+24y^{2}+11y^{2}+44y+6y+24-120$$

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

$$y^{4}+10y^{3}+35y^{2}+44y+6y+24-120$$

Combine 44y and 6y to get 50y.

$$y^{4}+10y^{3}+35y^{2}+50y+24-120$$

Subtract 120 from 24 to get -96.

$$y^{4}+10y^{3}+35y^{2}+50y-96$$

Expand

$$y^{4}+10y^{3}+35y^{2}+50y-96$$

Solution Steps

Apply the distributive property by multiplying each term of y+1 by each term of y+2.

$$\left(y^{2}+2y+y+2\right)\left(y+3\right)\left(y+4\right)-120$$

Combine 2y and y to get 3y.

$$\left(y^{2}+3y+2\right)\left(y+3\right)\left(y+4\right)-120$$

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

$$\left(y^{3}+3y^{2}+3y^{2}+9y+2y+6\right)\left(y+4\right)-120$$

Combine 3y^{2} and 3y^{2} to get 6y^{2}.

$$\left(y^{3}+6y^{2}+9y+2y+6\right)\left(y+4\right)-120$$

Combine 9y and 2y to get 11y.

$$\left(y^{3}+6y^{2}+11y+6\right)\left(y+4\right)-120$$

Apply the distributive property by multiplying each term of y^{3}+6y^{2}+11y+6 by each term of y+4.

$$y^{4}+4y^{3}+6y^{3}+24y^{2}+11y^{2}+44y+6y+24-120$$

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

$$y^{4}+10y^{3}+24y^{2}+11y^{2}+44y+6y+24-120$$

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

$$y^{4}+10y^{3}+35y^{2}+44y+6y+24-120$$

Combine 44y and 6y to get 50y.

$$y^{4}+10y^{3}+35y^{2}+50y+24-120$$

Subtract 120 from 24 to get -96.

$$y^{4}+10y^{3}+35y^{2}+50y-96$$