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    hiya people,
    can you help me with these couple of questions from an old gcse paper please? it would be a great help

    1.Factorise y^2-9z^2

    2. Express x^2+12x-5 in the form (x+a)^2

    thanks
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    i dont get da first one cos its got ys and z's
    but the second one is completing the square - the answer is- (x+6)² -41
    (i think!!)
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    (Original post by lucasharrison)
    hiya people,
    can you help me with these couple of questions from an old gcse paper please? it would be a great help

    1.Factorise y^2-9z^2

    2. Express x^2+12x-5 in the form (x+a)^2

    thanks
    1. y²-9z² => (y + 3z)(y - 3z) [ difference of 2 squares ]

    2. x²+12x-5 => (x + 6)² - 36 - 5 => (x + 6)² - 41

    [ I know the second isn't in the desired form but I don't think that the form without a +/- b is possible ]

    edit: correction.
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    (Original post by samdavyson)
    1. y²-9z² => (y + 3z)(y - 3z) [ difference of 2 squares ]

    2. x²+12x-5 => (x + 6)² - 36 + 5 => (x + 6)² - 31

    [ I know the second isn't in the desired form but I don't think that the form without a +/- b is possible ]
    i think uve done the 2nd one rong???? (x+6)² gives u x²+12x+36. we want -5. so to get to -5 from +36 you have to -41.
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    (Original post by darth_vader05)
    i think uve done the 2nd one rong???? (x+6)² gives u x²+12x+36. we want -5. so to get to -5 from +36 you have to -41.
    Yes you are quite right. Corrected above.
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    (Original post by lucasharrison)
    2. Express x^2+12x-5 in the form (x+a)^2

    thanks
    Alternative interpretation of (x+a)^2

    (x + 6)² - 31 is not of the form (x+a)², so it doesn't seem to answer the question (unless the question is wrong, of coourse)

    If we use the quadratic formula, then we get two answers, giving a result like (x + p ± q)². But the question doesn't ask for it be given in that form.

    So, a, in the answer can be one of the roots (from using the quadraric formula) and I'm assuming that a should have a +ve value.


    use the quadratic formula,

    x^2+12x-5 = 0
    x = -6 ± √(36 + 5)
    x = -6 ± √41
    x = -6 - √41, x = -6 + √41
    x = -a, x = b

    where
    a = 6 + √41, (a +ve quantity)
    b = -6 + √41 (a -ve quantity)

    x^2+12x-5 = (x + a)² = (x + 6 + √41)²
    =============================
 
 
 
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