Question

The sum of the coefficients in the binomial expansion of ${\left(\frac{1}{x}+2x\right)}^6$ is equal to

• A. 1024
• B. 729
• C. 243
• D. 512
• E. 64

Answer 1

Answer: (B)

${\left(\frac{1}{x}+2x\right)}^6={\left(\frac{1}{x}\right)}^6+{}^6{C}_1{\left(\frac{1}{x}\right)}^5(2x{)}^1+{}^6{C}_2{\left(\frac{1}{x}\right)}^4$
$(2x{)}^2+{}^6{C}_3{\left(\frac{1}{x}\right)}^3(2x{)}^3+{}^6{C}_4{\left(\frac{1}{x}\right)}^2(2x{)}^4$
$+{}^6{C}_5\left(\frac{1}{x}\right)(2x{)}^5+{}^6{C}_6(2x{)}^6$
$={\left(\frac{1}{x}\right)}^6+12{\left(\frac{1}{x}\right)}^4+60{\left(\frac{1}{x}\right)}^2+160$
$+240(x{)}^2+192(x{)}^4+64(x{)}^6$
$\therefore$ Sum of coefficients
$=1+12+60+160+240+192+64$
$=729$