Date: Sun, 7 Mar 1999 15:42:55 -0600 (CST)
Sender: firstname.lastname@example.org (LSivad)
Subject: factoring a differance of a trimonimal square
Who is asking: Student
Hi,m2 + 6m + 9
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
and I try to factor it. Factoring gives me
m2 + 6m + 9 = (m + 3)2
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).
m2+6m+9-n2 = (m + 3)2 - n2 = (m + 3 - n)(m + 3 + n)
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