In Exercises 15–58, find each product. (5−7x)(5+7x)

Verified step by step guidance

1. Recognize that the expression \((5 - 7x)(5 + 7x)\) is a difference of squares.
2. Recall the formula for the difference of squares: \((a - b)(a + b) = a^2 - b^2\).
3. Identify \(a = 5\) and \(b = 7x\) in the expression.
4. Apply the difference of squares formula: \((5)^2 - (7x)^2\).
5. Simplify the expression to get \(25 - 49x^2\).

Key Concepts

Factoring Difference of Squares

The expression (a - b)(a + b) represents the difference of squares, which simplifies to a² - b². In this case, a is 5 and b is 7x. Recognizing this pattern allows for a quick and efficient way to multiply the two binomials without distributing each term individually.

Binomial Multiplication

Binomial multiplication involves multiplying two binomials, which can be done using the distributive property or the FOIL method (First, Outside, Inside, Last). This method ensures that all combinations of terms from both binomials are accounted for, leading to the correct product.

Combining Like Terms

After multiplying the binomials, the resulting expression may contain like terms, which are terms that have the same variable raised to the same power. Combining these terms simplifies the expression, making it easier to interpret and use in further calculations.