How do you multiply (x^(1/3)+x^(-1/3))^2(x13+x13)2?

1 Answer
Sep 6, 2016

x^(2/3)+2+x^(-2/3)x23+2+x23

Explanation:

(x^(1/3)+^(-1/3))^2=(x^(1/3)+x^(-1/3))(x^(1/3)+x^(-1/3))(x13+13)2=(x13+x13)(x13+x13)

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+x13)(x13+x13)

=color(red)(x^(1/3))(x^(1/3)+x^(-1/3))color(red)(+x^(-1/3))(x^(1/3)+x^(-1/3))=x13(x13+x13)+x13(x13+x13)

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)