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Thread: Simplifying Expressions

  1. #16
    Super Member Quacky's Avatar
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    Re: Simplifying Expressions

    Quote Originally Posted by richtea9 View Post
    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!

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

    $\displaystyle =x^2+4$
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  2. #17
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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?
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  3. #18
    Super Member Quacky's Avatar
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    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 $\displaystyle -2\times{-2}=+4$
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  4. #19
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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?
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  5. #20
    Super Member Quacky's Avatar
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    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:
    $\displaystyle (x+7)(x+3)-(x+3)^2$
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  6. #21
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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
    Last edited by richtea9; Oct 22nd 2011 at 11:16 AM.
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  7. #22
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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?
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  8. #23
    Super Member Quacky's Avatar
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    Re: Simplifying Expressions

    Quote Originally Posted by richtea9 View Post
    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.
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  9. #24
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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:

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

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

    $\displaystyle -6+x^2$
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  10. #25
    Super Member Quacky's Avatar
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    Re: Simplifying Expressions

    Quote Originally Posted by richtea9 View Post
    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.
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  11. #26
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    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
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  12. #27
    Super Member Quacky's Avatar
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    Re: Simplifying Expressions

    Quote Originally Posted by richtea9 View Post
    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.
    Then, just combine your terms.

    So, pair them like before:
    $\displaystyle x^2-x^2=0$
    ...etc.
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  13. #28
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    Re: Simplifying Expressions

    Quote Originally Posted by Quacky View Post
    Great start!

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

    First, distribute that negative sign to the last set of brackets.
    Then, just combine your terms.

    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?
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  14. #29
    Super Member Quacky's Avatar
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    Re: Simplifying Expressions

    Quote Originally Posted by richtea9 View Post
    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
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  15. #30
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    Re: Simplifying Expressions

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

    Thank you so much! I really appreciate it.
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