Solve 2y^2(y+2)+13y(y+2)+15(y+2)

$$2 y ^ { 2 } ( y + 2 ) + 13 y ( y + 2 ) + 15 ( y + 2 )$$

Evaluate

$$\left(y+2\right)\left(y+5\right)\left(2y+3\right)$$

Solution Steps

Use the distributive property to multiply 2y^{2} by y+2.

$$2y^{3}+4y^{2}+13y\left(y+2\right)+15\left(y+2\right)$$

Use the distributive property to multiply 13y by y+2.

$$2y^{3}+4y^{2}+13y^{2}+26y+15\left(y+2\right)$$

Combine 4y^{2} and 13y^{2} to get 17y^{2}.

$$2y^{3}+17y^{2}+26y+15\left(y+2\right)$$

Use the distributive property to multiply 15 by y+2.

$$2y^{3}+17y^{2}+26y+15y+30$$

Combine 26y and 15y to get 41y.

$$2y^{3}+17y^{2}+41y+30$$

Expand

$$2y^{3}+17y^{2}+41y+30$$

Solution Steps

Use the distributive property to multiply 2y^{2} by y+2.

$$2y^{3}+4y^{2}+13y\left(y+2\right)+15\left(y+2\right)$$

Use the distributive property to multiply 13y by y+2.

$$2y^{3}+4y^{2}+13y^{2}+26y+15\left(y+2\right)$$

Combine 4y^{2} and 13y^{2} to get 17y^{2}.

$$2y^{3}+17y^{2}+26y+15\left(y+2\right)$$

Use the distributive property to multiply 15 by y+2.

$$2y^{3}+17y^{2}+26y+15y+30$$

Combine 26y and 15y to get 41y.

$$2y^{3}+17y^{2}+41y+30$$