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# Maths past paper question

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1. 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. 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.
3. 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. (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. a = 2?
6. (Original post by Sir_Malc)
a = 2?
Yep
7. 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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