Date: Sun, 7 Mar 1999 15:42:55 -0600 (CST)
To: QandQ@MathCentral.uregina.ca
Sender: sivad@canada.com (LSivad)
Subject: factoring a differance of a trimonimal square
Name: LSivad
Who is asking: Student
Level: Secondary
Question:
m(squared)+6m+9-n(squared)
Hi,
I believe that facility in algebra is to a large extent seeing patterns as it is in geometry. The first pattern to look for is a common factor. There is no common factor here so next look for groups of terms that look familar. You may need to rewrite the expression and change the order to see this. In your problem I see a pattern in the grouping
m2 + 6m + 9
and I try to factor it. Factoring gives me
m2 + 6m + 9 = (m + 3)2
Thus
m2+6m+9-n2 = (m + 3)2 - n2
The pattern I see here is
a2 - b2
which factors as
a2 - b2=(a - b)(a + b).
Thus
m2+6m+9-n2 = (m + 3)2 - n2 = (m + 3 - n)(m + 3 + n)
Cheers
Penny
Go to Math Central
To return to the previous page use your browser's back button.
|