Solve 2y^0(y+2)+13y(y+2)+15(y+2)

$$2 y ^ { 0 } ( y + 2 ) + 13 y ( y + 2 ) + 15 ( y + 2 )$$

Evaluate

$$\left(y+2\right)\left(13y+17\right)$$

Solution Steps

Calculate y to the power of 0 and get 1.

$$2\times 1\left(y+2\right)+13y\left(y+2\right)+15\left(y+2\right)$$

Multiply 2 and 1 to get 2.

$$2\left(y+2\right)+13y\left(y+2\right)+15\left(y+2\right)$$

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

$$2y+4+13y\left(y+2\right)+15\left(y+2\right)$$

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

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

Combine 2y and 26y to get 28y.

$$28y+4+13y^{2}+15\left(y+2\right)$$

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

$$28y+4+13y^{2}+15y+30$$

Combine 28y and 15y to get 43y.

$$43y+4+13y^{2}+30$$

Add 4 and 30 to get 34.

$$43y+34+13y^{2}$$

Factor

$$\left(y+2\right)\left(13y+17\right)$$

Solution Steps

Factor out common term y+2 by using distributive property.

$$\left(y+2\right)\left(2y^{0}+13y+15\right)$$

Consider 2y^{0}+13y+15. Simplify.

$$13y+17$$

Rewrite the complete factored expression.

$$\left(y+2\right)\left(13y+17\right)$$