3.2 Binomial Expansions

Write out the binomial expansions of $\left(x+2\right)^4$  

•  $-x^4+8x^3+24x^2+32x+16$  

•  $-x^4-8x^3-24x^2-32x-16$  

•  $x^4+8x^3+24x^2+32x+16$  

•  $x^4-8x^3-24x^2-32x-16$  

Write out the binomial expansions of $\left(1-3x\right)^3$  

•  $1+9x-27x^2+27x^3$  

•  $1−9x+27x^2−27x^3$  

•  $1+9x+27x^2+27x^3$  

•  $-1−9x+27x^2−27x^3$  

Find the first three terms of the binomial expansions $\left(\frac{1}{x}+2x\right)^6$  

•  $\frac{1}{x^6}+\frac{12}{x^4}+\frac{60}{x^2}+...$  

•  $-\frac{1}{x^6}+\frac{12}{x^4}+\frac{60}{x^2}+...$  

•  $\frac{1}{x^6}-\frac{12}{x^4}-\frac{60}{x^2}-...$  

•  $\frac{1}{x^6}+\frac{12}{x^4}-\frac{60}{x^2}+...$  

Find the first three terms of the binomial expansions $\left(\frac{1}{x^2}+x^3\right)^7$  

•  $-\frac{1}{x^{14}}+\frac{7}{x^9}-\frac{21}{x^4}+....$  

•  $-\frac{1}{x^{14}}-\frac{7}{x^9}-\frac{21}{x^4}+....$  

•  $\frac{1}{x^{14}}+\frac{7}{x^9}+\frac{21}{x^4}+....$  

•  $\frac{1}{x^{14}}-\frac{7}{x^9}-\frac{21}{x^4}+....$  

Find the coefficient of the $x^2$  term in the expansion of  $\left(2x+\frac{1}{x}\right)^{10}$  

•  $13440x^2$  

•  $-13440x^2$  

•  $1344x^2$  

•  $-1344x^2$  

Find the coefficient of the  $x^4$ term in the expansion of  $\left(\frac{x}{2}-\frac{3}{x}\right)^8$  

•  $-\frac{60}{16}x^4$  

•  $\frac{60}{16}x^4$  

•  $-\frac{63}{16}x^4$  

•  $\frac{63}{16}x^4$  

Find the term independent of x in the expansion of $\left(x^2+\frac{5}{x^3}\right)^{15}$  

• -78,203,125

• 78,203,125

• 5005

• -5005

Expand $\frac{1}{\left(3-x\right)^3}$  up to term $x^3$  and determine the interval of x for which the expansion is valid.

•  $\frac{1}{27}+\frac{1}{27}x+\frac{2}{81}x^2+\frac{10}{729}x^3+...$  
  Valid for  $-3<x<3$  

•  $\frac{1}{27}-\frac{1}{27}x+\frac{2}{81}x^2-\frac{10}{729}x^3+...$  
  Valid for $\left|-\frac{1}{3}x\right|<1$  

•  $\frac{1}{27}+\frac{1}{27}x+\frac{2}{81}x^2+\frac{10}{729}x^3+...$  
  
  Valid for  $-\frac{1}{3}<x<\frac{1}{3}$  

Expand $\left(1+3x\right)^{\frac{1}{3}}$  up to term $x^3$  and determine the interval of x for which the expansion is valid.

•  $1+x-x^2+\frac{5}{3}x^3+...$  
  Valid for  $-\frac{1}{3}<x<\frac{1}{3}$  

•  $1+x+x^2+\frac{5}{3}x^3+...$  
  Valid for $\left|-\frac{1}{3}x\right|<1$  

•  $1+x-x^2+\frac{5}{3}x^3+...$  
  Valid for  $-3<x<3$  

Find the term independent of x in the expansion of $\left(x^2-\frac{3}{x^2}\right)^{10}$  

• -61,236

• 61,236

• -60,236

• 60,236