\( 1 \leftarrow \begin{array}{l}\text { Multiply. } \\ (4 b+5)(4 b-5) \\ (4 b+5)(4 b-5)=\square \text { (Simplify your answer.) }\end{array} \)

To multiply \( (4b + 5)(4b - 5) \), you can use the difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \). Here, let \( a = 4b \) and \( b = 5 \). So, applying the formula: \[ (4b + 5)(4b - 5) = (4b)^2 - (5)^2 = 16b^2 - 25. \] There you go! The simplified expression is \( 16b^2 - 25 \). This multiplication showcases a fundamental algebraic concept that has been used since ancient times! The difference of squares formula is a classic result that simplifies calculations and is prevalent in various math topics, from basic algebra to polynomial identities. It's a neat shortcut that saves time and effort! To avoid common pitfalls in multiplying polynomials, remember to apply the distributive property carefully. A common mistake is to incorrectly multiply each term. Double-check that each term gets multiplied with every other term in the binomials to ensure you're not missing any terms. You'll master multiplying polynomials in no time with a bit of practice!