Simplify (x + 2)(x - 3) + x.

Step-by-step solution

1. 1

   Expand the product first. Order of operations puts multiplication before the outer addition:

   $(x+2)(x-3)=x(x-3)+2(x-3)=x^2-3x+2x-6$

2. 2

   Combine inside the expansion. $-3x+2x=-x$, so

   $(x+2)(x-3)=x^2-x-6$

3. 3

   Bring in the loose $+x$.

   $x^2-x-6+x$

4. 4

   Cancel the linear terms. $-x+x=0$, which removes the linear term completely:

   $x^2-6$

   The cancellation is not a coincidence here: the product $(x+2)(x-3)$ has middle coefficient $2+(-3)=-1$, and adding $x$ neutralises exactly that.

5. 5

   Check at two values. At $x=0$: $(2)(-3)+0=-6$, and $0-6=-6$ $\checkmark$. At $x=4$: $(6)(1)+4=10$, and $16-6=10$ $\checkmark$. As a bonus, $x^2-6$ is a difference of squares over the reals: $(x-\sqrt6)(x+\sqrt6)$.