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# Find the coefficient of the term x^3 in the expansion of (2+3x)^3 x (5-x)^3

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1. I get the answer to be 26 but apparently the answer is -143, im not sure where ive gone wrong and would appreciate it if someone can tell me what i've done, thanks..
2. (Original post by supersakkysuk)
I get the answer to be 26 but apparently the answer is -143, im not sure where ive gone wrong and would appreciate it if someone can tell me what i've done, thanks..
You are adding the x^3 coefficient of the first bracket (27) to the x^3 bracket of the second bracket (-1).

The questions wants you to multiply the backets together

Spoiler:
Show

How can we make x^3 coeffiecients?

Multiplying the x^3 coefficient of the first bracket the the x^0 coefficient of the second.

The x^2 coefficient by the x^1 coefficient.

x^1 by x^2
x^0 by x^3

3. When in doubt, multiply it out manually using the grid method
4. (Original post by supersakkysuk)
I get the answer to be 26 but apparently the answer is -143, im not sure where ive gone wrong and would appreciate it if someone can tell me what i've done, thanks..
using the nCr formula:
do 3C0 of the left multiplied by 3C3 of the right
plus 3C1 of left multiplied by 3C2 of the right
plus 3C2 of left multiplied by 3C1 of the right
plus 3C3 of left multiplied by 3C0 of the right

collecte the x^3 terms of all four and it should make -143 I think.
5. [QUOTE=offhegoes;64804739]You are adding the x^3 coefficient of the first bracket (27) to the x^3 bracket of the second bracket (-1).

The questions wants you to multiply the backets together
Spoiler:
Show

How can we make x^3 coeffiecients?

Multiplying the x^3 coefficient of the first bracket the the x^0 coefficient of the second.

The x^2 coefficient by the x^1 coefficient.

x^1 by x^2
x^0 by x^3

I have worked through it again and get the answer to be -143, thank you for the help
using the nCr formula:
do 3C0 of the left multiplied by 3C3 of the right
plus 3C1 of left multiplied by 3C2 of the right
plus 3C2 of left multiplied by 3C1 of the right
plus 3C3 of left multiplied by 3C0 of the right

collecte the x^3 terms of all four and it should make -143 I think.

Yes it does, i have since done it and got -143, thank you
7. (Original post by supersakkysuk)
Yes it does, i have since done it and got -143, thank you
you're welcome

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