How do you multiply (x^(1/3)+x^(-1/3))^2(x13+x−13)2?
1 Answer
Explanation:
(x^(1/3)+^(-1/3))^2=(x^(1/3)+x^(-1/3))(x^(1/3)+x^(-1/3))(x13+−13)2=(x13+x−13)(x13+x−13) 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))(x13+x−13)(x13+x−13)
=color(red)(x^(1/3))(x^(1/3)+x^(-1/3))color(red)(+x^(-1/3))(x^(1/3)+x^(-1/3))=x13(x13+x−13)+x−13(x13+x−13) now distribute the brackets
color(blue)"--------------------------------------------------------------"-------------------------------------------------------------- We require to use the
color(blue)"laws of exponents"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)