Answer: The solutions for the factored expression are:
y = -9z/4 and y = 9z/4.
Explanation:
To factor and solve the expression 16y^2 - 81z^2, we can recognize that it is a difference of squares. The formula for factoring a difference of squares is (a^2 - b^2) = (a + b)(a - b).
In this case, we have 16y^2 - 81z^2, which can be expressed as (4y)^2 - (9z)^2. Now, we can see that a = 4y and b = 9z.
Using the formula for factoring a difference of squares, we can factor the expression as follows:
16y^2 - 81z^2 = (4y + 9z)(4y - 9z)
Now we have factored the expression into two binomial terms: (4y + 9z) and (4y - 9z).
To solve the factored expression, we can set each binomial term equal to zero and solve for the variables:
Setting 4y + 9z = 0, we can solve for y:
4y = -9z
y = -9z/4
Setting 4y - 9z = 0, we can solve for y:
4y = 9z
y = 9z/4 Therefore, the solutions for the factored expression are:
y = -9z/4 and y = 9z/4.