Question
Find the product. Simplify your answer. \( (2 k+3)(2 k-3) \)
Ask by Reyes Little. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product is \(4k^2 - 9\).
Solution
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Beyond the Answer
To find the product \( (2k+3)(2k-3) \), we can use the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). In this case, let \( a = 2k \) and \( b = 3 \). So we have: \[ (2k + 3)(2k - 3) = (2k)^2 - (3)^2 \] Calculating that gives us: \[ (2k)^2 = 4k^2 \quad \text{and} \quad (3)^2 = 9 \] Thus, we have: \[ 4k^2 - 9 \] So the simplified answer is \( \boxed{4k^2 - 9} \).
