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Math Help - Expanding Quadratic Expressions (Answers needed)

  1. #1
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    Expanding Quadratic Expressions (Answers needed)

    1) Expand and Simplify

    (4x-3)(x+5)


    2) Prove that

    (n+5)^2 - (n+3)^2 = 4(n+4)


    3)

    a) Expand and simplify (2n+1)^2

    b) Prove that the square of any odd number is always 1 more than a multiple of 8.


    4) Expand and simplify (x-3)(2x+1)


    5)

    a) Expand and simplify (x+y)(x-y)

    b) Using your answer to part (a). or otherwise, find the exact value of
    780^2 - 220^2
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  2. #2
    Pim
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    What have you tried yourself? What do you have problems with?
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  3. #3
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    Could you perhaps give a brief step by step guide as to what to do?

    I missed alot of work on this and i'm struggling. Thanks.
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  4. #4
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    1) Multiply 1st term in first bracket by 1st term in second bracket
    Add to this, the product of the 1st term in the 1st bracket and the 2nd term in the 2nd bracket
    Add to this, the product of the 2nd term in the 1st bracket and the 1st term in the 2nd bracket
    Add to this, the product of the 2nd term in the 1st bracket and the 2nd term in the 2nd bracket

    2) Can you expand the two brackets on the left?

    We'll do the others after those.
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  5. #5
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    1)

    4x * x = 4x^2
    4x * 5 = 20x
    -3 * x = -3x
    -3 * 5 = -15

    = 4x^2 + 20x -3x -15

    Correct so far?
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Yes, you simplify now, taking the part containing: 20x - 3x
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  7. #7
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    8x + 17x - 15?
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  8. #8
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    Great! Next number now.
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  9. #9
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    How do you expand the two brackets on the left? >_<
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Just like you did for the first one.


    (n+5)^2 - (n+3)^2 = (n+5)(n+5) - (n+3)(n+3)

    You'll notice that if you have something of the type:

    (a+b)^2

    It expands in the fom:

    a^2 + 2ab + b^2

    But for the time being, expand it like you did for 1)
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  11. #11
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    Whilst doing this, do I ignore the powers?
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  12. #12
    MHF Contributor Unknown008's Avatar
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    You already took the powers into consideration.

    Doesn't

    5^2 = 5\times5 = 25

    x^2 = x \times x

    Similarly,

    (n+5)^2 = (n+5)(n+5)
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  13. #13
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    (n+5)^2 - (n+3)^2

    n x n = n^2
    n x 3 = 3n
    5 x n = 5n
    5 x 3 = 15

    n^2 + 3n + 5n + 15
    = N^2 + 8n + 15

    Did i do it right? :S
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  14. #14
    MHF Contributor Unknown008's Avatar
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    No, you didn't get my point.

    First expand (n+5)^2.

    Then expand (n+3)^2.

    Lastly, subtract the two expansions.
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  15. #15
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    Quote Originally Posted by Roxas View Post
    (n+5)^2 - (n+3)^2

    n x n = n^2
    n x 3 = 3n
    5 x n = 5n
    5 x 3 = 15

    n^2 + 3n + 5n + 15
    = N^2 + 8n + 15

    Did i do it right? :S
    No. If you want to do it by expanding each term, then you need to recall that (a + b)^2 = a^2 + 2ab + b^2. After correctly expanding, you then need to correctly take the difference. It should be clear, for example, that the final answer will NOT include n^2 ....

    I suggest you get a copy of the class notes that you missed and review them carefully. Your textbook will also have exmaples that you should carefully review.
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