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Maths past paper question

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    Can anyone please give me advice on how to work out the following question:

    Here is an identity:

    (2x + a)(x + 3) == 2X^2 + 4ax +b

    a and b are numbers.

    Work out b.
    I got the first line right by multiplying out the first part with the brackets as follows:

    2x^2 + 6x + ax + 3a

    Any idea on what to do next?

    Any help is appreciated as I have an exam tomorrow.
  2. Offline

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    Compare coefficients.
    From observation you can see that 6x + ax = 4ax which you can then solve to find A.
    You can then see that the constant term b is the product of 3 and A so 3a = b.
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    For the 6x + ax = 4ax part, you have to solve it by grouping all the 'a parts' on one side don't you, and then factorise it?

    So you'd do this:

    6x +ax = 4ax
    6x = 3ax
    0 = 3ax - 6x
    0 - 3x(a - 2)

    is that right?
  4. Offline

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    (Original post by Sir_Malc)
    For the 6x + ax = 4ax part, you have to solve it by grouping all the 'a parts' on one side don't you, and then factorise it?

    So you'd do this:

    6x +ax = 4ax
    6x = 3ax
    0 = 3ax - 6x
    0 - 3x(a - 2)

    is that right?
    Yes, so what do you know about the expression a-2?
  5. Offline

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    a = 2?
  6. Offline

    ReputationRep:
    (Original post by Sir_Malc)
    a = 2?
    Yep :yep:
  7. Offline

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    ah, so you substitute that back into the original quadratic and you end up with b = 6 at the end.

    Thank you very much both of you for the help.

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