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Yep, pretty basic stuff i know but i need to know if i have done this correctly as its part of a bigger question regarding a bigger expression, am just not sure on this part.

Basically i have the following expression:

$$-3(x-2)^2$$

And i need to expand and simplify it, the way i've done it is below but am not sure if it is correct

First i start by dealing with the exponent which is 2:

$-3(x-2)^2 = -3(x-2)(x-2)$ (Not sure if there should be another -3)

Then i expand each of the terms in the brackets with the -3 on the outside which i don't know if it is correct because am not sure if you can multiply both of the brackets by just the -3 alone since it's only outside the first bracket (hence my first point)

$$-3(x-2)(x-2) = -3x + 6 -3x + 6$$

I then proceed to simplify $-3x + 6 -3x + 6$ and get

$$9x^2 -18x - 18x + 36$$

And then i simplify $9x^2 -18x - 18x + 36$ to get:

$$9x^2 - 36x^2 + 36$$

I just get the feeling i haven't done this properly

If someone could help explain if this is correct or not and give advice if it isn't then that would be very appreciated

(Oh not sure if the tag is correct either if someone wants to correct it)

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Ok so you first solve $(x-2)^2=(x-2)(x-2)=x(x-2)-2(x-2)=x^2-2x-2x+4=x^2-4x+4$

$$-3(x-2)^2 = -3(x^2-4x+4) = -3x^2+12x-12$$

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  • $\begingroup$ While this is true, it doesn't really help the OP find and overcome the misunderstandings in his solution attempt. $\endgroup$
    – hmakholm left over Monica
    Sep 7, 2016 at 21:07
  • $\begingroup$ I get this for the most part, just not quite sure how you manipulated the bracket to end up with 4x + 4, i understand the rest $\endgroup$
    – Zochonis
    Sep 7, 2016 at 21:10

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