I need a step by step explanation of finding the GCF of (6ysquare -3y)(y+7)

The greatest common factor, or GCF, is the greatest factor that divides two numbers. ... If there are no common factors, the GCF is 1.

That is the situation on your case.
6y^2 -3y and y+7 do not have common factors.

To find the GCF of the given expression (6ysquare -3y)(y+7), we can follow these steps:

Step 1: Factor each term individually.

The first term, 6ysquare, can be factored as the product of 6, y, and y. So, 6ysquare = 6 * y * y.

The second term, -3y, does not have any common factors.

The third term, y + 7, is already in factored form.

Therefore, the given expression can be expressed as (6 * y * y - 3 * y)(y + 7).

Step 2: Group the common factors.

Now, we can group the common factors from the expression. In this case, the common factor is y, which appears in both terms. Grouping the common factor, we get:

y * (6y - 3)(y + 7).

Step 3: Simplify the expression.

We can simplify further by multiplying the terms inside the parentheses:

y * (6y - 3) = 6y^2 - 3y

Therefore, the simplified expression is 6y^2 - 3y * (y + 7).

Step 4: Check for any common factors.

Now, we can check if there are any common factors between the terms in the expression. In this case, there are no common factors between the terms 6y^2 - 3y and y + 7.

Step 5: Determine the GCF.

Since there are no common factors, the GCF of the expression (6ysquare -3y)(y+7) is 1.

In summary, the GCF of (6ysquare -3y)(y+7) is 1.

(6ysquare -3y)(y+7)

= (3y) (2y - 1) (y+7)