Question

what is the product of the two binomials below? (4a + 5b)(4a - 5b) a. 16a² - 25b² b. 4a² - 5b² c. 4a² + 5b² d. 16a² + 25b²

Explanation:

Step1: Apply difference - of - squares formula

Use the formula $(a + b)(a - b)=a^{2}-b^{2}$, where $a = 4A$ and $b = 5B$.

Step2: Calculate $a^{2}$ and $b^{2}$

$a^{2}=(4A)^{2}=16A^{2}$, $b^{2}=(5B)^{2}=25B^{2}$.

Step3: Find the product

$(4A + 5B)(4A - 5B)=16A^{2}-25B^{2}$.

Answer:

A. $16A^{2}-25B^{2}$