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Expanding Triple Brackets
Seems quite a trivial question, but I've never really known the method to expand triple brackets. Can obviously expand double brackets (would be a little stuffed otherwise) but would be great if somebody could help out. Use this as an example:
(x + 4)(x - 1)(x - 3)
Probably simpler than I think.
Cheers,
-Will
(x + 4)(x - 1)(x - 3)
Probably simpler than I think.
Cheers,
-Will
Expand 2 of them to get a quadratic in 1.
(x + 4)(x^2 - 4x + 3)
Then expand that.
x^3 - 4x^2 + 3x + 4x^2 - 16x + 12
And simply.
x^3 - 13x + 12
(x + 4)(x^2 - 4x + 3)
Then expand that.
x^3 - 4x^2 + 3x + 4x^2 - 16x + 12
And simply.
x^3 - 13x + 12
(x + 4)(x - 1)(x - 3)
(x^2 + 3x - 4)(x-3)
x^3 + 3x^2 -4x - 3x^2 - 9x + 12
x^3 - 13x + 12
edit: didin't see the negative sign.
(x^2 + 3x - 4)(x-3)
x^3 + 3x^2 -4x - 3x^2 - 9x + 12
x^3 - 13x + 12
edit: didin't see the negative sign.
Codefusion
(x + 4)(x + 1)(x - 3)
(x^2 + 5x + 4)(x-3)
x^3 + 5x^2 + 4x - 3x^2 - 15x - 12
x^3 + 2x^2 - 11x - 12
(x^2 + 5x + 4)(x-3)
x^3 + 5x^2 + 4x - 3x^2 - 15x - 12
x^3 + 2x^2 - 11x - 12
Should be (x - 1)
MrTrig
Should be (x - 1)
yeah sorry bout that , i edited anyways.
Hi! Just noticed that none of the answers use the method that I learnt. I saw this while searching for a worksheet and thought I would share my knowledge.
Start the same as before, by expanding one set of brackets:
(x +4 )(x^2 - 4x + 3)
Then, you can expand in a different way to make the next step easier.
If you had say, 3x + 12, you would say it is equal to 3x + 3(4), so you would factorise it as 3(x + 4).
You can rewrite the first equation as (x^2 - 4x + 3)(x + 4).
There, you can see that the (x^2 - 4x + 3) equates to the 3 in the factorising example.
Therefore, (x + 4)(x^2 - 4x + 3) can also be written as x (x^2 - 4x + 3) + 4 (x^2 -4x +3).
From there, you can simply expand it normally and collect like terms.
Therefore, your full working would be:
(x + 4)(x - 1)(x - 3)
(x + 4)(x^2 - 4x + 3)
x(x^2 - 4x + 3) + 4(x^2 - 4x + 3)
x^3 - 4x^2 + 3x + 4x^2 - 16x + 12
x^3 - 13x + 12
Start the same as before, by expanding one set of brackets:
(x +4 )(x^2 - 4x + 3)
Then, you can expand in a different way to make the next step easier.
If you had say, 3x + 12, you would say it is equal to 3x + 3(4), so you would factorise it as 3(x + 4).
You can rewrite the first equation as (x^2 - 4x + 3)(x + 4).
There, you can see that the (x^2 - 4x + 3) equates to the 3 in the factorising example.
Therefore, (x + 4)(x^2 - 4x + 3) can also be written as x (x^2 - 4x + 3) + 4 (x^2 -4x +3).
From there, you can simply expand it normally and collect like terms.
Therefore, your full working would be:
(x + 4)(x - 1)(x - 3)
(x + 4)(x^2 - 4x + 3)
x(x^2 - 4x + 3) + 4(x^2 - 4x + 3)
x^3 - 4x^2 + 3x + 4x^2 - 16x + 12
x^3 - 13x + 12
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