SOLUTION: Factor 6b^2-24b+24=? The correct answer is 6 (b-2)^2 but can you explain?

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Question 1184036: Factor 6b^2-24b+24=?
The correct answer is 6 (b-2)^2 but can you explain?
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Factor 6b^2-24b+24=?
The correct answer is 6 (b-2)^2 but can you explain?
:
Factor out 6
6(b^2 - 4b + 4)
this is a perfect square which can be factored to
6(b-2)(b-2)
which is
6(b-2)^2

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your expression is 6b^T2 - 24b + 24

factor out the 6 to get:

6 * (b^2 - 4b + 4)

factor b^2 - 4b + 4 to get (b-2)^2.

you are left with 6 * (b-2)^2.

factoring b^2 - 4b + 4 can be done in several ways.

if you can't do it any other way, then use the quadratic formula.

i just happened to know that (b-2)^2 is equal to (b-2) * (b-2) which is equal to b * (b-2) - 2 * (b-2) which is equal to b^2 - 2b -2b + 4 which is equal to b^2 - 4b + 4.

here's a reference on solving quadratics you might find helpful.

https://www.purplemath.com/modules/solvquad6.htm

the quadratic formula is in the section titled "formula".