Find each product. (14r-1)(17r+2)

Verified step by step guidance

1. Identify the two binomials to be multiplied: \((14r - 1)\) and \((17r + 2)\).
2. Apply the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second binomial: First, Outer, Inner, Last.
3. Multiply the First terms: \(14r \times 17r\).
4. Multiply the Outer terms: \(14r \times 2\) and the Inner terms: \(-1 \times 17r\).
5. Multiply the Last terms: \(-1 \times 2\), then combine all these products and simplify by combining like terms.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. It states that a(b + c) = ab + ac. This property is essential for expanding expressions like (14r - 1)(17r + 2) by multiplying each term in the first parenthesis by each term in the second.

Combining Like Terms

After expanding an expression, combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies the expression into a more manageable form, such as combining terms with 'r' or constant terms.

Multiplying Binomials

Multiplying binomials involves applying the distributive property twice or using the FOIL method (First, Outer, Inner, Last) to multiply each term in the first binomial by each term in the second. This process results in a polynomial expression.