I am looking factoring with the distributive property.

4m^2 + 4mp + 3mp + 3p^2

You have a few options...

If you group the terms then you will have a common factor at the end.
(4m^2 + 4mp)+ (3mp + 3p^2)
This should get you started : )

Or... just put your 4mp and 3mp together and factor the trinomial : )

4m^2 + 7mp + 3p^2

I guess using distributive property backwards :)

4m (m+p)
+
3p (m+p)

=(4m+3p)(m+p)

To factor the expression 4m^2 + 4mp + 3mp + 3p^2 using the distributive property, we can look for common factors among the terms.

First, let's group the terms with a common factor together:

(4m^2 + 4mp) + (3mp + 3p^2)

Now, we factor out the common factors from each group:

4m(m + p) + 3p(m + p)

Notice that both groups have a factor of (m + p). Now, we can factor out (m + p) from the expression:

(m + p)(4m + 3p)

So the fully factored form of 4m^2 + 4mp + 3mp + 3p^2 using the distributive property is (m + p)(4m + 3p).