Find each product. (5−7x)(5+7x)

Verified step by step guidance

1. Recognize that the expression (5−7x)(5+7x) 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 \(a = 5\) and \(b = 7x\) in the given expression.
4. Apply the formula by squaring each term: calculate \(a^2 = (5)^2\) and \(b^2 = (7x)^2\).
5. Write the product as \(5^2 - (7x)^2\), which simplifies to \(25 - 49x^2\).

Key Concepts

Binomial Multiplication

Binomial multiplication involves multiplying two expressions, each with two terms, such as (a + b)(c + d). The distributive property is used to multiply each term in the first binomial by each term in the second, combining like terms to simplify the result.

Difference of Squares

The difference of squares is a special product formula: (a - b)(a + b) = a² - b². It applies when multiplying conjugate binomials, resulting in the square of the first term minus the square of the second term, simplifying the multiplication process.

Combining Like Terms

After multiplying binomials, terms with the same variable and exponent are combined to simplify the expression. This step ensures the final answer is in its simplest form, making it easier to interpret or use in further calculations.