Thread: My dad is horrible at math

I just figured this out now. And he's a pediatrician. He can't offer me anyhelp in this subject. I guess thats where my bad math skills came from. I have a test tommorow and I'M still not understanding FOIL or how to factor an expression such as 100b^2 + 180b + 81 into (10b+9)^2
or 4x^2 - 81y^2 into (2x+9y)(2x-9y)

Please and way of solving these problems into the easiest way is welcomed. I really hope I don't fail this math test but Im just not grasping this stuff im having an off week in math.

The last one first because I think it is the easiest. any time we have a difference of squares ex.(x^2 - y^2) it will factor as (x+y)* (x-y)

ex. x^2 - 4 is also the differance of squares. x^2 = x*x and 4 = 2*2
So it will factor (x+2)*(x-2)

In your example 4x^2-81y^2 notice that 4=2*2 and x^2=x*x and 81=9*9 and y^2=y*y.

Do you see that every number is a square?
So we will take 2x from the first term and 9y from the last term and put it into the form (x+y)*(x-y) and we get (2x+9y)*(2x-9y) So this is called a Difference Of Squares

The first problem is called a perfect square. Notice that the first and last term are squares. The first term 100b^2 = 10*10*b*b and the last term is 81=9*9.
But notice that the middle term is equal to 10*b*9*2 or 180b

Let me show you
(10b+9)^2= (10b +9)*(10b+9)
Using FOIL we get
First 10b*10b =100b^2
Outside 10b*9 = 90b (please notice that we will do this one more time)
Inside 9*10b= 90b
Last 9*9=81

The inside and outside terms are added together and in a Perfect Square both the inside and outside terms are the same

So when we factor a Perfect Square (sometimes refered to as a Trinomial Square) the general form is
A^2 +2AB +B^2 = (A+B)^2 and
A^2 -2AB +B^2 = (A-B)^2

So finally back to your problem 100b^2 + 180b +81 where 100=10*10 and b^2=b*b and 180b= 2*90b and 81=9*9 we get (10b+9)^2

Hope this helps

One more thing FOIL means First Outside Inside Last, it describes the order in which we multiply these factors ex (a+b)*(c+d)
1. miltiply the First terms a and c
2. multiply the Outside terms a and d
3. multiply the Inside terms b and c
4. miltiply the Last terms b and d