Sue Pemberton Solutions for Chapter: Series, Exercise 4: EXERCISE 6B

Find the coefficient of x³ in each of the following expansions.

${\left(1+3\mathrm{x}\right)}^{12}$

Find the coefficient of $x^3$ in each of the following expansions.

${\left(2+\frac{\mathrm{x}}{4}\right)}^7$

Find the coefficient of $x^3$ in each of the following expansions.

${\left(3-\frac{\mathrm{x}}{3}\right)}^{10}$

Find the coefficient of ${\mathrm{x}}^4$ in the expansion of ${\left(2\mathrm{x}+1\right)}^{12}$.

Find the term in x⁵ in the expansion of ${(5-2\mathrm{x})}^8$.

Find the coefficient of x⁸y⁵ in the expansion of ${(\mathrm{x}-2\mathrm{y})}^{13}$.

Find the term independent of $x$ in the expansion of ${\left(\mathrm{x}-\frac{3}{{\mathrm{x}}^2}\right)}^{12}$.

Hence, obtain the coefficient of x² in the expansion of $(2+3\mathrm{x}-{\mathrm{x}}^2){\left(1-\frac{\mathrm{x}}{2}\right)}^8$.