Factor the expression 16x^2-72xy+81y^2 into a product of binomials.
The given expression is a perfect square:
(4x - 9y)^2 = (4x - 9y)(4x - 9y).
To factor the expression 16x^2 - 72xy + 81y^2, we need to look for two binomials in the form (ax + by)(cx + dy) that multiply together to give us the original expression.
The first step is to find the factors of the first and last terms of the expression. In this case, the factors of 16x^2 are 4x and 4x, and the factors of 81y^2 are 9y and 9y.
Next, we need to determine the signs of these factors in order to obtain the middle term, -72xy. Since the middle term is negative, we know that one of the factors must be positive, and the other must be negative.
Now, we can rewrite the middle term (-72xy) by splitting it into two parts using the factors we found: -8xy and -64xy.
The expression 16x^2 - 72xy + 81y^2 can now be written as:
(4x - 9y)(4x - 9y)
So, the factored form of the expression is (4x - 9y)^2.