How do you multiply #(x^(1/3)+x^(-1/3))^2#?

1 Answer
Sep 6, 2016

Answer:

#x^(2/3)+2+x^(-2/3)#

Explanation:

#(x^(1/3)+^(-1/3))^2=(x^(1/3)+x^(-1/3))(x^(1/3)+x^(-1/3))#

We must ensure when multiplying that each term in the 2nd bracket is multiplied by each term in the 1st bracket.
This can be done as follows.

#(color(red)(x^(1/3)+x^(-1/3)))(x^(1/3)+x^(-1/3))#

#=color(red)(x^(1/3))(x^(1/3)+x^(-1/3))color(red)(+x^(-1/3))(x^(1/3)+x^(-1/3))#

now distribute the brackets
#color(blue)"--------------------------------------------------------------"#

We require to use the #color(blue)"laws of exponents"#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(a^mxxa^n=a^(m+n)" and " a^0=1)color(white)(a/a)|)))#
#color(blue)"------------------------------------------------------------------"#

#=x^(1/3+1/3)+x^(1/3-1/3)+x^(-1/3+1/3)+x^(-1/3-1/3)#

#=x^(2/3)+x^0+x^0+x^(-2/3)#

#=x^(2/3)+1+1+x^(-2/3)=x^(2/3)+2+x^(-2/3)#