Group two terms of the trinomial to rewrite them as the sum of two quantities.
Always
Practice makes perfect
Let's consider a binomial m_1+m_2 and a trinomial t_1+t_2+t_3. Our job is to see if we can multiply them by using the FOIL method.
(m_1+m_2)(t_1+t_2+t_3)
According to the F O I L method, to multiply two binomials we find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms.
As we can see, the method above works for two binomials. In our case we have one trinomial, but it is not a problem since we can rewrite our trinomial as the sum of two expressions by grouping two of its terms.
t_1+t_2+t_3 = (t_1+t_2) + t_3
By taking (t_1+t_2) as one single term we can apply the FOIL method.
After this first multiplication is performed, we get the following expression.
m_1(t_1+t_2)_F + m_1t_3_O + m_2(t_1+t_2)_I + m_2t_3_L
We continue by applying the Distributive Property and simplifying. As a consequence, we can always apply the FOIL method to multiply a binomial and a trinomial and the given statement is always true.
