Multiply the binomials.
$(3m+4n)(3m-4n)$

• A. $3n^2-4n^2$
• B. $9m^2+24mn-16n^2$
• C. $9m^2-24mn-16n^2$
• D. $9m^2-16n^2$

Answer: (D)

Verified step by step guidance

1. Recognize that the expression \((3m + 4n)(3m - 4n)\) is a product of two binomials in the form of \((a + b)(a - b)\), which is a difference of squares pattern.
2. Recall the difference of squares formula: \((a + b)(a - b) = a^2 - b^2\).
3. Identify \(a = 3m\) and \(b = 4n\) from the given binomials.
4. Square each term separately: \(a^2 = (3m)^2 = 9m^2\) and \(b^2 = (4n)^2 = 16n^2\).
5. Apply the difference of squares formula to write the product as \$9m^2 - 16n^2$.