Solve 3(a+h)^2-(a+h)+3

$$3 ( a + h ) ^ { 2 } - ( a + h ) + 3$$

Evaluate

$$3\left(a+h\right)^{2}-a-h+3$$

Solution Steps

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

$$3\left(a^{2}+2ah+h^{2}\right)-\left(a+h\right)+3$$

Use the distributive property to multiply 3 by a^{2}+2ah+h^{2}.

$$3a^{2}+6ah+3h^{2}-\left(a+h\right)+3$$

To find the opposite of a+h, find the opposite of each term.

$$3a^{2}+6ah+3h^{2}-a-h+3$$

Expand

$$3a^{2}+6ah-a+3h^{2}-h+3$$

Solution Steps

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

$$3\left(a^{2}+2ah+h^{2}\right)-\left(a+h\right)+3$$

Use the distributive property to multiply 3 by a^{2}+2ah+h^{2}.

$$3a^{2}+6ah+3h^{2}-\left(a+h\right)+3$$

To find the opposite of a+h, find the opposite of each term.

$$3a^{2}+6ah+3h^{2}-a-h+3$$