Factor the expression completely.45x−18y+36
First, we can factor out the greatest common factor (GCF) of the expression, which is 9:
45x - 18y + 36 = 9(5x - 2y + 4)
Therefore, the expression can be factored completely as 9(5x - 2y + 4).
To factor the expression 45x - 18y + 36 completely, we can start by finding the greatest common factor (GCF) of all the terms. In this case, the GCF is 9.
So, we can rewrite the expression as:
9(5x - 2y + 4)
Now, the expression is fully factored.
To factor the expression completely, we need to find the greatest common factor (GCF) of all the terms and then factor it out. Let's break down each term to identify the common factors.
45x = 5 * 9 * x
-18y = -2 * 3 * 3 * y
36 = 2 * 2 * 3 * 3
Now, let's look for the shared factors. We find that 3 is a common factor for all the terms. We can factor out the GCF, which is 3.
Factoring out 3 from each term:
45x = 3 * 5 * 9 * x ÷ 3 = 5 * 9 * x = 45x
-18y = -2 * 3 * 3 * y ÷ 3 = -2 * 3 * y = -6y
36 = 2 * 2 * 3 * 3 ÷ 3 = 2 * 2 * 3 = 12
So, factoring the expression completely, we have:
45x - 18y + 36 = 3(15x - 6y + 12)
Therefore, the expression 45x - 18y + 36 factors completely as 3(15x - 6y + 12).