Question

4p^2+12pq+9q^2 I need to factor this problem

Answer 1

(2p+3q)^2

Answer 2

how did you get that answer. Please show me so i can possibly understand

Answer 3

Ok this is how you would do this problem:

4p^2+12pq+9q^2

Notice that 4p^2 is a perfect square: (2p)^2
and
Notice that 9q^2 is a perfect square: (3q)^2

Next we have to figure out 12pq

If you multiply them together you will get 36p^2 q^2. Now if you take the square root of this (6pq) and double it you get the middle term: 12pq

This means that the factored problem is (2p+3q)^2

Any time the middle term is twice the square root of the product of the other two terms, and those other terms are perfect squares, the whole thing is a perfect square.

Answer 4

okay thanks that makes sense to me.