Expand and simplify ${{\left( 3-\frac{1}{3}x \right)}^{4}}$ in ascending powers of $x$. Given th

Question

Expand and simplify ${{\left( 3-\frac{1}{3}x \right)}^{4}}$ in ascending powers of $x$. Given that the coefficients of $x$ and ${{x}^{2}}$ in the expansion of $\left( 1+ax+b{{x}^{2}} \right){{\left( 3-\frac{1}{3}x \right)}^{4}}$ are $126$ and $-187\frac{1}{2}$ respectively, calculate the value of $a$ and of $b$.

Accepted Answer

$81-36x+6x^2-\frac{4}{9}x^3+\frac{1}{81}x^4$ $a=2,\ b=-\frac{3}{2}$

Binomial Theorem - Binomial Expansion for Positive Integer Powers

Binomial Theorem - Binomial Expansion for Positive Integer Powers

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