Find each product. See Examples 3–5. (14r-1)(17r+2)

Verified step by step guidance

1. Apply the distributive property, also known as the FOIL method, to multiply the two binomials: $(14r-1)(17r+2)$.
2. First, multiply the first terms of each binomial: $14r\times 17r$.
3. Next, multiply the outer terms: $14r\times 2$.
4. Then, multiply the inner terms: $-1\times 17r$.
5. Finally, multiply the last terms: $-1\times 2$, and combine all the results to form a single expression.

Key Concepts

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process is often referred to as the FOIL method for binomials, which stands for First, Outside, Inside, Last. Understanding how to properly distribute terms is essential for finding the product of polynomials.

Combining Like Terms

After multiplying polynomials, the next step is to combine like terms, which are terms that have the same variable raised to the same power. This simplification process helps in expressing the polynomial in its simplest form. Recognizing and correctly combining these terms is crucial for accurate results.

Standard Form of a Polynomial

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. This format makes it easier to analyze and compare polynomials. Understanding how to write a polynomial in standard form is important for clarity and further mathematical operations.