If the coefficient of $x^{3}$ $x^3$ in the expansion of $(2 + x) {(3 - a x)}^{4}$ $(2 + x)(3 - ax)^4$ is 30, how do you find the values of the constant a?

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If the coefficient of $x^{3}$ $x^3$ in the expansion of $(2 + x) {(3 - a x)}^{4}$ $(2 + x)(3 - ax)^4$ is 30, how do you find the values of the constant a?

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Answer 1 · 2015-12-23T16:48:19

$a = 1$ $a=1$

Explanation:

Simply expand the expression and make it in the form of a polynomial
then you get the coefficient of $x^{3}$ $x^3$ as $(54 a^{2} - 24 a^{3})$ $(54a^2-24a^3)$ which is equal to 30
$54 a^{2} - 24 a^{3} = 30$ $54a^2-24a^3=30$
$a^{2} (54 - 24 a) = 30$ $a^2(54-24a)=30$
which gives $a = 1$ $a=1$

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If the coefficient of $x^{3}$ $x^3$ in the expansion of $(2 + x) {(3 - a x)}^{4}$ $(2 + x)(3 - ax)^4$ is 30, how do you find the values of the constant a?

1 Answer

Explanation:

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If the coefficient of $x^{3}$ $x^3$ in the expansion of $(2 + x) {(3 - a x)}^{4}$ $(2 + x)(3 - ax)^4$ is 30, how do you find the values of the constant a?