1. ## Re: Simplifying Expressions

Originally Posted by richtea9
Ok, I've been working on the following expression to see if I could get the right result.

$\displaystyle (x-2)^2+4x$

So I first do:

$\displaystyle (x-2)(x-2)$ = $\displaystyle x^2-2x-2x-4+4x$ = $\displaystyle x^2-4$

So I think the result is this? $\displaystyle x^2-4$

If this is wrong, hopefully you should be able to see the thought process I have gone through and figure out what I'm doing wrong.
Almost, but you made the same mistake as last time!

$\displaystyle (x-2)(x-2)+4x=x^2-2x-2x{\color{red}+}4+4x$

$\displaystyle =x^2+4$

2. ## Re: Simplifying Expressions

Originally Posted by Quacky
Almost, but you made the same mistake as last time!

$\displaystyle (x-2)(x-2)+4x=x^2-2x-2x{\color{red}+}4+4x$

$\displaystyle =x^2+4$
Ok, thanks again.

Why is the minus after the last 2x becoming a plus?

3. ## Re: Simplifying Expressions

It should never have been a minus - this was a small mistake you made when using FOIL on the brackets.
You have $\displaystyle -2\times{-2}=+4$

4. ## Re: Simplifying Expressions

Originally Posted by Quacky
It should never have been a minus - this was a small mistake you made when using FOIL on the brackets.
You have $\displaystyle -2\times{-2}=+4$
Ah OK! I think I'm getting it now, thank you. Could you possibly provide me with another expression to make sure?

5. ## Re: Simplifying Expressions

Sure! Have a crack at some of these:

$\displaystyle x^2-(x+2)(x+4)$

$\displaystyle (x-3)^2-9$

Fairly challenging, perhaps:
$\displaystyle (x+7)(x+3)-(x+3)^2$

6. ## Re: Simplifying Expressions

Originally Posted by Quacky
Sure! Have a crack at some of these:

$\displaystyle x^2-(x+2)(x+4)$

$\displaystyle (x-3)^2-9$

Fairly challenging, perhaps:
$\displaystyle (x+7)(x+3)-(x+3)^2$
Rethinking

7. ## Re: Simplifying Expressions

Originally Posted by Quacky
Sure! Have a crack at some of these:

$\displaystyle x^2-(x+2)(x+4)$

$\displaystyle (x-3)^2-9$

Fairly challenging, perhaps:
$\displaystyle (x+7)(x+3)-(x+3)^2$
Ok for the first one I did this:

$\displaystyle (x+2)(x+4)$ = $\displaystyle x^2+4x+2x+6$ = $\displaystyle x^2+6x+6$

$\displaystyle x^2-(x^2+6x+6)$

$\displaystyle x^2-x^2 = 0$

So we left with $\displaystyle 6x+6$

EDIT: I'm thinking that maybe when joining 4x and 2x together, you multiply them together? so 8?

8. ## Re: Simplifying Expressions

Originally Posted by richtea9
Ok for the first one I did this:

$\displaystyle (x+2)(x+4)$ = $\displaystyle x^2+4x+2x+{\color{red}8}$ = $\displaystyle x^2+6x+{\color{red}8}$

$\displaystyle x^2-(x^2+6x+{\color{red}8})$

$\displaystyle x^2-x^2 = 0$

So we left with $\displaystyle -(6x+{\color{red}8})$
You made a silly mistake, but otherwise you were nearly there. Again, you just need to remember that if you have something like $\displaystyle -(6x+8)$, this means $\displaystyle -6x-8$ because you have to distribute the negative to every term inside the brackets.

9. ## Re: Simplifying Expressions

Originally Posted by Quacky
You made a silly mistake, but otherwise you were nearly there. Again, you just need to remember that if you have something like $\displaystyle -(6x+8)$, this means $\displaystyle -6x-8$ because you have to distribute the negative to every term inside the brackets.
Ok, I understand that now

For the second one I did the following:

$\displaystyle (x-3)^2 = (x-3)(x-3) = x^2-3x-3x+9 = x^2-6x+9$

$\displaystyle (x^2-6x+9)-9 = -6+x^2$

$\displaystyle -6+x^2$

10. ## Re: Simplifying Expressions

Originally Posted by richtea9
Ok, I understand that now

For the second one I did the following:

$\displaystyle (x-3)^2 = (x-3)(x-3) = x^2-3x-3x+9 = x^2-6x+9$

$\displaystyle (x^2-6x+9)-9 = -6{\color{red}x}+x^2$

$\displaystyle -6{\color{red}x}+x^2$
Another silly mistake! You are the master of them. The working out stages were fine though.

11. ## Re: Simplifying Expressions

Originally Posted by Quacky
Another silly mistake! You are the master of them. The working out stages were fine though.
Ah, I wrote it into the computer, thats what I had on paper

Ok the last one is difficult.

$\displaystyle (x+7)(x+3) = x^2+10x+21$

$\displaystyle (x+3)^2 = (x+3)(x+3) = x^2+6x+9$

I'm not sure what to do after this stage

12. ## Re: Simplifying Expressions

Originally Posted by richtea9
Ah, I wrote it into the computer, thats what I had on paper

Ok the last one is difficult.

$\displaystyle (x+7)(x+3) = x^2+10x+21$

$\displaystyle (x+3)^2 = (x+3)(x+3) = x^2+6x+9$

I'm not sure what to do after this stage
Great start!

$\displaystyle (x^2+10x+21)-(x^2+6x+9)$

First, distribute that negative sign to the last set of brackets.

So, pair them like before:
$\displaystyle x^2-x^2=0$
...etc.

13. ## Re: Simplifying Expressions

Originally Posted by Quacky
Great start!

$\displaystyle (x^2+10x+21)-(x^2+6x+9)$

First, distribute that negative sign to the last set of brackets.

So, pair them like before:
$\displaystyle x^2-x^2=0$
...etc.
Ok so

$\displaystyle x^2-x^2=0$

$\displaystyle 10x-6x=4x$

$\displaystyle 21-9=12$

Correct? I think I'm missing something! Properly the minus?

14. ## Re: Simplifying Expressions

Originally Posted by richtea9
Ok so

$\displaystyle x^2-x^2=0$

$\displaystyle 10x-6x=4x$

$\displaystyle 21-9=12$

Correct? I think I'm missing something! Properly the minus?
$\displaystyle 4x+12$ is correct. Well done

15. ## Re: Simplifying Expressions

Originally Posted by Quacky
4x+12 is correct. Well done
Perfecto!

Thank you so much! I really appreciate it.

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