FACTORIZATION BY GROUPING

y2+2y-5y-10
3x+ab+5ax+15ab?

y^2+2y-5y-10

= y(y + 2) - 5(y + 2)
= (y + 2)(y - 5)

the 2nd, 3x+ab+5ax+15ab
cannot be factored, I suspect a typo

Maybe you meant

3ax+ab+5ax+15ab
= 8ax + 16ab
= 8a(x+2b)

To factorize the expressions, we can use the method of "factoring by grouping."

Let's start with the first expression:
y^2 + 2y - 5y - 10

Step 1: Group the terms.
(y^2 + 2y) - (5y + 10)

Step 2: Find the greatest common factor (GCF) of each group.
In the first group, y is a common factor, and in the second group, 5 is a common factor.

Step 3: Factor out the GCF from each group.
y(y + 2) - 5(y + 2)

Step 4: Notice that both groups have a common factor of (y + 2).
(y - 5)(y + 2)

Therefore, the factored expression for y^2 + 2y - 5y - 10 is (y - 5)(y + 2).

Now let's look at the second expression:
3x + ab + 5ax + 15ab

Step 1: Group the terms.
(3x + ab) + (5ax + 15ab)

Step 2: Find the greatest common factor (GCF) of each group.
In the first group, there is no common factor other than 1, and in the second group, ax is a common factor.

Step 3: Factor out the GCF from each group.
(3x + ab) + ax(5 + 15b)

Step 4: Notice that both groups have a common factor of (3x + ab).
(3x + ab)(1 + ax)

Therefore, the factored expression for 3x + ab + 5ax + 15ab is (3x + ab)(1 + ax).

Remember, factoring by grouping involves grouping terms with common factors and then factoring out those common factors.