In Exercises 35–54, use the FOIL method to multiply the binomials. (4x+3)(5x+1)

Verified step by step guidance

1. Identify the two binomials: $(4x+3)$ and $(5x+1)$.
2. Apply the FOIL method, which stands for First, Outer, Inner, Last.
3. Multiply the First terms: $4x\times 5x$.
4. Multiply the Outer terms: $4x\times 1$.
5. Multiply the Inner terms: $3\times 5x$.

Key Concepts

Binomials

A binomial is a polynomial that consists of exactly two terms, which can be separated by a plus or minus sign. In the expression (4x + 3)(5x + 1), both (4x + 3) and (5x + 1) are binomials. Understanding binomials is essential for applying multiplication methods like FOIL.

FOIL Method

The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms: the first terms of each binomial, the outer terms, the inner terms, and the last terms. This systematic approach helps ensure that all products are accounted for in the final expression.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. After using the FOIL method to multiply the binomials, you may end up with multiple terms that can be combined to form a simpler expression. This step is crucial for arriving at the final answer.