1. ## Multiplying Binomials Quickly

Example 2
Using FOIL to find a product quickly
Find each product. Write down only the answer.
a) (x + 3)(x + 4)
a) (x + 3)(x + 4) = x2 + 7x + 12 Combine like terms: 3x + 4x = 7x.
I don't understand this. I get how they got 3x+4x=7x but i do not understand how that is equal to x2 + 7x + 12?

Using foil you get x2 + 7x + 12 if you combine like terms you get 3x + 4x = 7x I can't wrap my head around why these are equivelent statements.

2. Originally Posted by pkraus
Example 2
Using FOIL to find a product quickly
Find each product. Write down only the answer.
a) (x + 3)(x + 4)
a) (x + 3)(x + 4) = x2 + 7x + 12 Combine like terms: 3x + 4x = 7x.
I don't understand this. I get how they got 3x+4x=7x but i do not understand how that is equal to x2 + 7x + 12?

Using foil you get x2 + 7x + 12 if you combine like terms you get 3x + 4x = 7x I can't wrap my head around why these are equivelent statements.
x^2+4x+3x+12 is the same as x^2+7x+12

I hope this is what you were asking for!

3. I understand that what i don't understand is why ..

x^2 + 7x + 12

equal to

3x + 4x = 7x

4. Originally Posted by pkraus
I understand that what i don't understand is why ..

x^2 + 7x + 12

equal to

3x + 4x = 7x
They are not saying this at all. They are simply saying that when you expand, the terms you get include 3x + 4x. These terms are added to give 7x. It's as simple as that. They are simply explaining where the 7x has come from.

5. FOIL (x+ 3)(x+ 4)

F ("First times First"): $\displaystyle x*x= x^2$
O ("Outside times Outside"): $\displaystyle x*4= 4x$
I ("Inside times Inside"): $\displaystyle 3*x= 3x$
L ("last times Last"): 3*4= 12

Now add ALL of those: $\displaystyle x^2+ 4x+ 3x+ 12= x^2+ 7x+ 12$

"FOIL" involves 4 parts "4x+ 3x= 7x" is only two of those.