Solve 5(a+h)^2-5(a+h)-1

$$5 ( a + h ) ^ { 2 } - 5 ( a + h ) - 1$$

Evaluate

$$5\left(a+h\right)^{2}-5a-5h-1$$

Solution Steps

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

$$5\left(a^{2}+2ah+h^{2}\right)-5\left(a+h\right)-1$$

Use the distributive property to multiply 5 by a^{2}+2ah+h^{2}.

$$5a^{2}+10ah+5h^{2}-5\left(a+h\right)-1$$

Use the distributive property to multiply -5 by a+h.

$$5a^{2}+10ah+5h^{2}-5a-5h-1$$

Expand

$$5a^{2}+10ah-5a+5h^{2}-5h-1$$

Solution Steps

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

$$5\left(a^{2}+2ah+h^{2}\right)-5\left(a+h\right)-1$$

Use the distributive property to multiply 5 by a^{2}+2ah+h^{2}.

$$5a^{2}+10ah+5h^{2}-5\left(a+h\right)-1$$

Use the distributive property to multiply -5 by a+h.

$$5a^{2}+10ah+5h^{2}-5a-5h-1$$