In Exercises 83–94, find each product. (5x + 7y − 2)(5x + 7y + 2)

Key Concepts

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process is often facilitated by using the distributive property, which ensures that all combinations of terms are accounted for. In the given expression, each term in the first polynomial must be multiplied by each term in the second polynomial.

Difference of Squares

The expression (a - b)(a + b) represents the difference of squares, which simplifies to a² - b². This concept is crucial for recognizing patterns in polynomial multiplication, particularly when the polynomials are structured as a sum and difference of the same terms. In the provided question, recognizing this pattern can simplify the multiplication process.

Combining Like Terms

After multiplying polynomials, the next step is to combine like terms, which are terms that have the same variable raised to the same power. This process simplifies the expression into its most concise form. Understanding how to identify and combine like terms is essential for arriving at the final answer in polynomial expressions.