please answer !!!what is the product of the two binomials below?
(2A+3B)(2A-3B)
A. 4A²+ 9B²
B. 2A²- 3B²
C. 2A² + 3B²
D. 4A² - 9B²

Verified Answer :

Answer = D

Because:

(2A + 3B)(2A - 3B)
= 4A² - 6AB + 6AB - 9B²
= 4A² - 9B²

Answer: D. \(4A^2-9B^2\)

Step-by-step explanation:

Given expression : \((2A+3B)(2A-3B)\)

We know that there is an identity of product of two binomials :-

\((x+y)(x-y)=x^2-y^2\)

In the given expression , we have \(x=2A\text{ and}\ y=3B\)

Then by applying the above identity , we have

\((2A+3B)(2A-3B)=(2A)^2-(3B)^2\\\\=4A^2-9B^2\)