Find each product. See Example 5. (4r - 1) (7r + 2)

Verified step by step guidance

1. Identify the two binomials to be multiplied: \((4r - 1)\) and \((7r + 2)\).
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: \(4r \times 7r = 28r^{2}\).
4. Multiply the Outer terms: \(4r \times 2 = 8r\).
5. Multiply the Inner terms: \(-1 \times 7r = -7r\), and multiply the Last terms: \(-1 \times 2 = -2\). Then combine like terms \$8r\( and \)-7r$ to simplify the expression.

Key Concepts

Distributive Property

The distributive property allows you to multiply each term inside one parenthesis by each term inside the other. For example, in (a + b)(c + d), you multiply a by c and d, then b by c and d, combining all products.

Multiplying Binomials

Multiplying binomials involves applying the distributive property twice, often remembered as FOIL (First, Outer, Inner, Last). This method ensures all terms are multiplied correctly to form a polynomial.

Combining Like Terms

After multiplying, you combine like terms—terms with the same variable and exponent—to simplify the expression into its simplest polynomial form.