Use the distributive property to multiply $x$ by $x+1$.
$$x^{2}+x+8=\left(x+2\right)\left(x-2\right)$$
Consider $\left(x+2\right)\left(x-2\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $2$.
