Expand and simplify (x + 2)(x - 3).

Step-by-step solution

1. 1

   Distribute the first bracket term by term. Each term of $(x+2)$ multiplies the whole of $(x-3)$:

   $x(x-3) + 2(x-3)$

2. 2

   Expand both products.

   $x^2 - 3x + 2x - 6$

   These four terms are the F, O, I and L of the FOIL mnemonic: $x\cdot x$, $x\cdot(-3)$, $2\cdot x$, $2\cdot(-3)$.

3. 3

   Combine the two middle terms.

   $-3x + 2x = -x \quad\Longrightarrow\quad x^2 - x - 6$

   The middle coefficient is the sum of the two constants, $2 + (-3) = -1$, and the last term is their product, $2 \times (-3) = -6$ — the shortcut worth remembering for monic quadratics.

4. 4

   Read off the structure of the result. $x^2 - x - 6$ has roots $x = -2$ and $x = 3$, exactly the values that make each original factor vanish. Its graph is an upward parabola crossing the axis at those two points, with vertex at $x = \tfrac12$.

5. 5

   Check numerically at x = 5. The factored form gives $(7)(2) = 14$; the expanded form gives $25 - 5 - 6 = 14$. At $x = -1$: $(1)(-4) = -4$ and $1 + 1 - 6 = -4$. Both agree.