Expand (x + 2)(x + 5).

Step-by-step solution

1. 1

   Split the product using the distributive law. Treat $(x+5)$ as a single object multiplied by each term of the first bracket:

   $(x+2)(x+5)=x(x+5)+2(x+5)$

2. 2

   Distribute each piece.

   $x(x+5)=x^2+5x,\qquad 2(x+5)=2x+10$

   These four products are exactly the F, O, I, L of the mnemonic: First $x\cdot x$, Outer $x\cdot 5$, Inner $2\cdot x$, Last $2\cdot 5$.

3. 3

   Add and combine like terms.

   $x^2+5x+2x+10=x^2+7x+10$

4. 4

   Note the shortcut for monic binomials. When both brackets are $(x+p)$ and $(x+q)$, the answer is always $x^2+(p+q)x+pq$. Here $p+q=7$ and $pq=10$, which is why the middle coefficient is $7$ and the constant is $10$ — and it is exactly the pattern used in reverse when factoring.

5. 5

   Verify numerically. At $x=3$: $(5)(8)=40$, and $9+21+10=40$ $\checkmark$. At $x=-2$: $(0)(3)=0$, and $4-14+10=0$ $\checkmark$.