Use the FOIL method to multiply the binomials: (4x + 1)(3x + 2).

Step-by-step solution

1. 1

   Understand what FOIL organises. Every term of the first binomial must meet every term of the second. FOIL is just a bookkeeping order for those four products: First, Outer, Inner, Last.

2. 2

   First and Outer. First: $4x \cdot 3x = 12x^2$. Outer: $4x \cdot 2 = 8x$.

3. 3

   Inner and Last. Inner: $1 \cdot 3x = 3x$. Last: $1 \cdot 2 = 2$.

4. 4

   Combine like terms. Only the two middle products are alike: $8x + 3x = 11x$. The result is $12x^2 + 11x + 2$.

5. 5

   Check with a test value. At $x = 1$ the factors give $5 \cdot 5 = 25$, and the trinomial gives $12 + 11 + 2 = 25$.