Can't figure out the steps from (x - 3)^2 (1) + (x - 2)[2(x - 3)] to...

mickapoo

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I know the problem itself involves calculus, but I'm confused about the algebra that is involved here. Can someone tell me how they got from step 2 to step 3?

Thanks in advance :)
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I know the problem itself involves calculus, but I'm confused about the algebra that is involved here. Can someone tell me how they got from step 2 to step 3?

Thanks in advance :)
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2(x-2) = 2x -4
 
Yes, thank you.

Can anyone elaborate step-by-step on how they went from:

(x-3)^2 + (x-2)[2(x-3)]

to
(x-3)(x-3+2x-4)

Thank you in advance.
 
Yes, thank you.

Can anyone elaborate step-by-step on how they went from:

(x-3)^2 + (x-2)[2(x-3)]

to
(x-3)(x-3+2x-4)

Thank you in advance.

There's actually a few intermediate steps left out by the writer of this problem. I'd begin by rearranging the terms to make it a bit clearer what's happening:

(x-3)^2 + (x-2)[2(x-3)] = (x-3)^2 + (x-3)*(x-2)*2

Now, what happens if you factor out an (x-3) from the terms being added? Once you do that, Subhotosh Khan's hint will come into play.
 
Can anyone elaborate step-by-step on how they went from:

(x-3)^2 + (x-2)[2(x-3)]

to
(x-3)(x-3+2x-4)
Actually, they'd included a "(1)" to make it easier:

. . . . .(x - 3)2 (1) + (x - 2)[2(x - 3)]

What did you get when you took the common factor, being one copy of (x - 3), out front and simplified the rest?

. . . . .(x - 3) [(x - 3)(1) + (x - 2)(2)]

Where did you end up when you tried (not just "looked at") the algebra? ;)
 
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