Order of Operations for Solving Equations

Date: 10/12/95 at 17:26:18
From: Richard Seguin
Subject: Multiplying Binomials...

How would you multiply a question like this? -2(x-y)^2?

Date: 11/28/95 at 17:45:45
From: Doctor Rob
Subject: Re: Multiplying Binomials...

Hi Richard,

The principle to follow when doing algebraic manipulations like the above 
is to follow the "Order of Operations," which can be remembered as:

                     P.E.M.D.A.S.

1.  Parentheses
2.  Exponents
3.  Multiplication
4.  Division
5.  Addition
6.  Subtraction

In other words, do what is possible within parentheses first, then 
exponents, then multiplication and division (it doesn't matter what 
order), and then addition and subtraction (again, it doesn't matter 
what order).  

So say you're given a problem like this:  Evaluate 6(x - 4)^2

Step 1: Nothing to do in parentheses, so evaluate the binomial

6(x - 4)^2 = 6(x^2 - 8*x +16)  [recall that (x - y)^2 = x^2 - 2xy + y^2]

Step 2: Apply the distributive property of multiplication [a(b+c) = 
ab + ac]

6(x^2 - 8*x +16) = 6*x^2 - 6*8*x + 6*16

Step 3: Do the multiplication

                 = 6*x^2 - 48*x + 96

I hope this helps you with your problem.  Work it through and see if you 
get the answer -2x^2 + 4xy - 2y^2.

-Doctor Rob,  The Geometry Forum