Factorise 4y2+24y+32 completely.

Sure, here are the steps to factorise the given expression:

1. First, we look for the greatest common factor (GCF) in all the terms. In this case, the GCF is 4. So, we factor out 4 from each term:

   4y² + 24y + 32 = 4(y² + 6y + 8)

2. Now, we need to factorise the quadratic expression inside the parentheses. We are looking for two numbers that multiply to 8 (the constant term) and add up to 6 (the coefficient of y). The numbers 2 and 4 fit these conditions. So, we can write:

   y² + 6y + 8 = (y + 2)(y + 4)

3. Substituting this back into the expression we factored out the 4 from, we get:

   4(y² + 6y + 8) = 4(y + 2)(y + 4)

So, the factorised form of 4y² + 24y + 32 is 4(y + 2)(y + 4).