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