Find each product. (8s-3t)(8s+3t)

Verified step by step guidance

1. Recognize that the expression \((8s - 3t)(8s + 3t)\) is a product of two binomials in the form \((a - b)(a + b)\), which is a difference of squares pattern.
2. Recall the difference of squares formula: \((a - b)(a + b) = a^2 - b^2\).
3. Identify \(a = 8s\) and \(b = 3t\) from the given expression.
4. Square each term separately: \(a^2 = (8s)^2 = 64s^2\) and \(b^2 = (3t)^2 = 9t^2\).
5. Apply the difference of squares formula to write the product as \(64s^2 - 9t^2\).

Key Concepts

Difference of Squares Formula

The difference of squares formula states that (a - b)(a + b) = a² - b². It is used to simplify the product of two binomials that are conjugates, where the middle terms cancel out, leaving the difference between the squares of the two terms.

Binomial Multiplication

Binomial multiplication involves multiplying two expressions each containing two terms. This can be done using the distributive property (FOIL method), where each term in the first binomial is multiplied by each term in the second binomial.

Exponents and Squaring Terms

Squaring a term means multiplying it by itself, which increases the exponent by two. For example, (8s)² = 64s². Understanding how to square coefficients and variables correctly is essential when applying formulas like the difference of squares.