The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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:


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

Associated Topics:
Middle School Algebra

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.