Final answer:
To factor the expression completely, we can factor out the greatest common factor and then find two binomials that multiply to give the expression. The factored form is 4(x + 4.5y)(x + 4.5y).
Step-by-step explanation:
We are given the expression 4x2 + 36cy + 81y2. To factor this expression completely, we need to find two binomials where the product of their terms equals the given expression. We can start by factoring out the greatest common factor, which is 4:
4x2 + 36cy + 81y2 = 4(x2 + 9cy + 20.25y2)
Next, we need to find two numbers that multiply to give 20.25 and add up to 9c. The numbers are 4.5y and 4.5y, so we can write:
4(x + 4.5y)(x + 4.5y)
Finally, we can simplify the expression to:
4(x + 4.5y)(x + 4.5y)