Solve 2(a+h)^2+4(a+h)+5

$$2 ( a + h ) ^ { 2 } + 4 ( a + h ) + 5$$

Evaluate

$$2\left(a+h\right)^{2}+4a+4h+5$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+h\right)^{2}.

$$2\left(a^{2}+2ah+h^{2}\right)+4\left(a+h\right)+5$$

Use the distributive property to multiply 2 by a^{2}+2ah+h^{2}.

$$2a^{2}+4ah+2h^{2}+4\left(a+h\right)+5$$

Use the distributive property to multiply 4 by a+h.

$$2a^{2}+4ah+2h^{2}+4a+4h+5$$

Expand

$$2a^{2}+4ah+4a+2h^{2}+4h+5$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+h\right)^{2}.

$$2\left(a^{2}+2ah+h^{2}\right)+4\left(a+h\right)+5$$

Use the distributive property to multiply 2 by a^{2}+2ah+h^{2}.

$$2a^{2}+4ah+2h^{2}+4\left(a+h\right)+5$$

Use the distributive property to multiply 4 by a+h.

$$2a^{2}+4ah+2h^{2}+4a+4h+5$$