uglyplushy
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when helen expands (ax+b)^3, she gets the coefficient of x to be 441 and the coefficient of x^2 to be 189. find the value of a/b.

i've expanded it to get:
a^3x^3 + 3a^2x^2b + 3axb^2 + b^3

i've ignored the first and last terms as they don't have x or x^2. i saw a 4 year old thread for this question so i made a new one, but i saw on that forum they did 3ab^2 = 441 and 3a^b = 189. i get that it is something to do with the coefficients of x, but could somebody explain why it is 3ab^2 = 441 and 3a^b = 189? i understand the rest of the process, except that part.

thanks
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ghostwalker
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(Original post by uglyplushy)
when helen expands (ax+b)^3, she gets the coefficient of x to be 441 and the coefficient of x^2 to be 189. find the value of a/b.

i've expanded it to get:
a^3x^3 + 3a^2x^2b + 3axb^2 + b^3

i've ignored the first and last terms as they don't have x or x^2. i saw a 4 year old thread for this question so i made a new one, but i saw on that forum they did 3ab^2 = 441 and 3a^b = 189. i get that it is something to do with the coefficients of x, but could somebody explain why it is 3ab^2 = 441 and 3a^b = 189? i understand the rest of the process, except that part.

thanks
In your expansion, the coefficient of x is 3ab^2. You're told the coeff. of x is 441. Hence they're equal. And in a similar manner x^2
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Dominininc
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A coefficient is a number or symbol multiplied with a variable or an unknown quantity in an algebraic term.

So question is telling you the coefficient is number is 441 and algebraic term is x.

However from the expansion we know the coefficient of x is 3ab^2.

Therefore these values must be equal so this can be written as 3ab^2 x = 441 x

Cancel the x's and you get 3ab^2 = 441
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0ptics
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(Original post by uglyplushy)
when helen expands (ax+b)^3, she gets the coefficient of x to be 441 and the coefficient of x^2 to be 189. find the value of a/b.

i've expanded it to get:
a^3x^3 + 3a^2x^2b + 3axb^2 + b^3

i've ignored the first and last terms as they don't have x or x^2. i saw a 4 year old thread for this question so i made a new one, but i saw on that forum they did 3ab^2 = 441 and 3a^b = 189. i get that it is something to do with the coefficients of x, but could somebody explain why it is 3ab^2 = 441 and 3a^b = 189? i understand the rest of the process, except that part.

thanks
They factorised the x^2 and x terms from 3a^2x^2b and 3axb^2 respectively.
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uglyplushy
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(Original post by Dominininc)
A coefficient is a number or symbol multiplied with a variable or an unknown quantity in an algebraic term.

So question is telling you the coefficient is number is 441 and algebraic term is x.

However from the expansion we know the coefficient of x is 3ab^2.

Therefore these values must be equal so this can be written as 3ab^2 x = 441 x

Cancel the x's and you get 3ab^2 = 441
(Original post by ghostwalker)
In your expansion, the coefficient of x is 3ab^2. You're told the coeff. of x is 441. Hence they're equal. And in a similar manner x^2
(Original post by 0ptics)
They factorised the x^2 and x terms from 3a^2x^2b and 3axb^2 respectively.
thank you so much everybody! i understand it now
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