Factor out the greatest common factor in the expression?

11y^5-55y^2

11y^2(y^3-5)

To factor out the greatest common factor in the given expression, 11y^5 - 55y^2, we first need to find the highest power of y that exists in both terms.

Step 1: Identify the coefficients:
The coefficients of the terms are 11 and -55.

Step 2: Identify the variable:
The variable in both terms is y.

Step 3: Identify the powers:
The powers of y are 5 and 2 in the two terms, respectively.

Now, let's find the greatest common factor (GCF) of the coefficients and the variable.

Step 4: Find the GCF of the coefficients:
The GCF of 11 and 55 is 11 because it is the largest number that divides both of them evenly.

Step 5: Find the GCF of the variable powers:
The GCF of 5 and 2 is 2 because it is the largest power of y that exists in both terms.

Step 6: Write the GCF as the common factor:
The GCF of the coefficients, 11, and the GCF of the powers, y^2, can be combined to form the common factor: 11y^2.

Step 7: Divide each term by the common factor:
To factor out the greatest common factor, we divide each term by the common factor, 11y^2:

11y^5 / 11y^2 = y^(5-2) = y^3
-55y^2 / 11y^2 = -5

Thus, the factored expression is 11y^5 - 55y^2 = 11y^2(y^3 - 5).