I would appreciate verification on the following: 1) Completely factor the expression: a^2 + 4b -ab - 4a (I have (a+b)(a-4) ) 2) completely factor r^2-2r+1 (I have r(r-2)+1 ) Thanks!

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- Jan 14th 2010, 08:45 PMjay1Please verify
I would appreciate verification on the following: 1) Completely factor the expression: a^2 + 4b -ab - 4a (I have (a+b)(a-4) ) 2) completely factor r^2-2r+1 (I have r(r-2)+1 ) Thanks!

- Jan 14th 2010, 09:07 PMbigwave
its easy to check these

just expand the brackets

$\displaystyle (a+b)(a-4) = a^2 - 4a + ba -4b$

which is not your original equation

the second one should be $\displaystyle (r-1)^2$ - Jan 14th 2010, 09:41 PMpickslides
- Jan 14th 2010, 10:46 PMnikhilkeep in mind
an equation in the form ax^2+bx+c=0 is called a quadratic equation. it can always be written as product of two factors.

1) a^2+4b-ab-4a

=a^2-ab+4b-4a

=a(a-b)+4(b-a)

=(a-b)(a-4) [there are two factors]

2)r^2-2r+1

=r^2-r-r+1

=r(r-1)-(r-1)

=(r-1)(r-1) (again two factors though equal)

=(r-1)^2

so before writing r(r-2)+1 remember quadratic equations can be written as product of two factors