Binomial Times Binomial

To multiply two binomials, such as $\left(x+2\right)\left(x+3\right)$, treat the first binomial as a single multiplier and distribute it over the second: $\left(x+2\right)x+\left(x+2\right)\cdot 3$. Then distribute each of those products in turn. Now every term of the first binomial has been multiplied by every term of the second: $x^{2}+3x+2x+6$.

Collect the middle terms to get $x^{2}+5x+6$. There are four products in all: the first terms, the outer terms, the inner terms and the last terms. Each pair of terms is multiplied once.

The two middle terms, $3x$ and $2x$, are the cross products. They add to $5x$. Their coefficient, 5, is the sum of 2 and 3, and the constant 6 is the product of 2 and 3. You will use this relationship to factor trinomials in the next section.