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Math Help - Factorising a quadratic

  1. #1
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    Factorising a quadratic

    I need help with factorising the following:

    a) (c+d)^2 - d^2

    I got c^2 + 2cd + d^2 - d^2 which is equal to c^2 + 2cd, is this correct please?

    b) 2w^2 + w - 3

    How do you do this again please (need simple and clear advice)? Thanks
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    I need help with factorising the following:

    a) (c+d)^2 - d^2

    I got c^2 + 2cd + d^2 - d^2 which is equal to c^2 + 2cd, is this correct please?

    b) 2w^2 + w - 3

    How do you do this again please (need simple and clear advice)? Thanks
    For the first one I think they wanted you to use the difference of squares.

    a^2-b^2=(a-b)(a+b) so in your case

    \underbrace{(c+d)^2}_{a^2}-\underbrace{d^2}_{b^2}=\underbrace{(c+d-d)}_{(a-b)}\underbrace{(c+d+d)}_{(a+b)}=c(c+2d)

    For b notice that

    2w^2+w-3=2w^2-2w+3w-3 and now factor by grouping.

    Notice to break up the middle term we found factors of 2(-3)=-6 that add up to the middle term -2w+3w=w
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  3. #3
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    Quote Originally Posted by Natasha1 View Post
    I need help with factorising the following:

    a) (c+d)^2 - d^2

    I got c^2 + 2cd + d^2 - d^2 which is equal to c^2 + 2cd, is this correct please?

    It's almost complete, notice that "c" is common...

    c(c+2d) is fully factored.

    Also, the method shown by TheEmptySet is very useful.


    b) 2w^2 + w - 3

    How do you do this again please (need simple and clear advice)? Thanks
    2w^2=2w(w)

    (2w+a)(w+b)=2w^2+w-3

    Examine "a" and "b" to find out how we get a single "w" after multiplying out the factors....

    ab=-3\Rightarrow\ a=3,\;b=-1;\;\;\;a=-3,\;b=1,\;\;\;a=1,\;b=-3,\;\;a=-1,\;\;b=3

    Since "b" will be multiplied by 2, we see that it needs to be -1

    2w^2+w-3=(2w+3)(w-1)
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  4. #4
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    here is how i did the first equation. (c+d)^{2} is a positive perfect square.

    (c+d)^{2}-d^{2}

    (c+d)(c+d)-d^{2}

    ({c}^{2}+2cd+{d}^{2})-{d}^2 expand perfect square.

    {c}^{2}+2cd collect d squared terms they cancel.

    c(c+2d) factor out c.
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