Expert: Paul Klarreich - 5/25/2008

Question
(a+b)^2=a^2+2ab+b^2 Can you please explain in easy english about what this formula is for and how it works. I am using the Oxford Level Eight Math Book and their explanation is hard to understand. Thanks!

Answer
Questioner:   Mehru
Category:  Advanced Math
Private:  No
 
Subject:  Algebra
Question:  (a+b)^2=a^2+2ab+b^2
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Hi, Mehru,

Can you please explain in easy english

>> Sorry, I only speak hard English -- with a capital E.

about what this formula is for and how it works. I am using the Oxford Level Eight Math Book

>> Serves you right -- get a real algebra book.  There are tons of them
and their explanation is hard to understand. Thanks!
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Now, then, this formula:

(a + b)^2 = a^2 + 2ab + b^2

is the rule for squaring a binomial.  It does two things:

1. shows you that when you square a binomial, like;

(x + 5)^2

you get THREE terms:
The first is the square of the first:  x^2
The last is the square of the last:  5^2 = 25
The middle is TWICE the cross-product: 2 times x times 5 = 10x

= x^2 + 10x + 25

2. Prevents you from making the child's error of thinking you just square the two terms.

3. Gets you started towards the method of completing the square.

OK, so I can't count up to 3.