Expand and simplify.
left parenthesis Start Root 2 x End Root plus Start Fraction 1 over x End Fraction right parenthesis cubed
(1 point)
Responses
2 x plus Start Fraction 2 over x End Fraction Start Root 2 x End Root plus Start Fraction 1 over x squared End Fraction
Image with alt text: 2 x plus Start Fraction 2 over x End Fraction Start Root 2 x End Root plus Start Fraction 1 over x squared End Fraction
2 x Start Root 2 x End Root plus Start Fraction 1 over x cubed End Fraction
Image with alt text: 2 x Start Root 2 x End Root plus Start Fraction 1 over x cubed End Fraction
left parenthesis Start Fraction 2 x cubed plus 2 over x squared End Fraction right parenthesis Start Root 2 x End Root plus Start Fraction 1 over x cubed End Fraction plus 4
Image with alt text: left parenthesis Start Fraction 2 x cubed plus 2 over x squared End Fraction right parenthesis Start Root 2 x End Root plus Start Fraction 1 over x cubed End Fraction plus 4
left parenthesis Start Fraction 2 x cubed plus 3 over x squared right parenthesis Start Root 2 x End Root plus Start Fraction 1 over x cubed End Fraction plus 6
The expanded and simplified expression is:
2x + 2√(2x) + 1/x^2
To expand and simplify the expression, we can apply the rules of exponents and combine like terms.
The given expression is:
(√(2x) + 1/x)^3
To expand (√(2x) + 1/x)^3, we can use the binomial theorem or simply distribute the cube to each term within the parentheses:
= (√(2x))^3 + 3(√(2x))^2(1/x) + 3(√(2x))(1/x)^2 + (1/x)^3
= (2x√(2x)) + 3(2x)(1/x) + 3(√(2x))(1/x^2) + (1/x^3)
= 2x√(2x) + 6 + 3(√(2x)/x) + 1/x^3
Simplifying further:
= 2x√(2x) + 1/x^3 + 3(√(2x)/x) + 6
Therefore, the expanded and simplified form is:
2x√(2x) + 1/x^3 + 3(√(2x)/x) + 6.