compleletly factor the following expression

9y^2-16z^2

It is the difference of two squares.

Use the standard rule
a^2 -b^2 = (a-b)(a+b)
The answer is
(3y -4z)(3y + 4z)

To completely factor the expression 9y^2 - 16z^2, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, the expression is 9y^2 - 16z^2. We can see that 9y^2 is a perfect square, as it is the square of 3y, and 16z^2 is also a perfect square, as it is the square of 4z.

Using the difference of squares formula, we can write the expression as:
(3y + 4z)(3y - 4z)

Therefore, the completely factored form of the expression 9y^2 - 16z^2 is (3y + 4z)(3y - 4z).