Solve 2(y+4)^2+5(y+4)-12

$$2 ( y + 4 ) ^ { 2 } + 5 ( y + 4 ) - 12$$

Evaluate

$$\left(y+8\right)\left(2y+5\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+4\right)^{2}.

$$2\left(y^{2}+8y+16\right)+5\left(y+4\right)-12$$

Use the distributive property to multiply 2 by y^{2}+8y+16.

$$2y^{2}+16y+32+5\left(y+4\right)-12$$

Use the distributive property to multiply 5 by y+4.

$$2y^{2}+16y+32+5y+20-12$$

Combine 16y and 5y to get 21y.

$$2y^{2}+21y+32+20-12$$

Add 32 and 20 to get 52.

$$2y^{2}+21y+52-12$$

Subtract 12 from 52 to get 40.

$$2y^{2}+21y+40$$

Expand

$$2y^{2}+21y+40$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+4\right)^{2}.

$$2\left(y^{2}+8y+16\right)+5\left(y+4\right)-12$$

Use the distributive property to multiply 2 by y^{2}+8y+16.

$$2y^{2}+16y+32+5\left(y+4\right)-12$$

Use the distributive property to multiply 5 by y+4.

$$2y^{2}+16y+32+5y+20-12$$

Combine 16y and 5y to get 21y.

$$2y^{2}+21y+32+20-12$$

Add 32 and 20 to get 52.

$$2y^{2}+21y+52-12$$

Subtract 12 from 52 to get 40.

$$2y^{2}+21y+40$$