Question

(x+1/x) ^3 expand the following​

Answer 1

Answer:

x³+1+3x(x+1)/x³ is the expanded form

Answer 2

We are asked to expand (x + 1/x)$^3{}$

We will solve it using identity (a + b)$^3{}$

$(a + b) {}^{3} = {a}^{3} + b {}^{3} + 3ab(a + b)$

$\Longrightarrow(x + \frac{1}{x} ) {}^{3} \\ \\ \\ = {x}^{3} + 3x {}^{2} \frac{1}{x} + 3x( \frac{1}{x} ) {}^{2} + ( \frac{1}{x} ) {}^{3}$

Now simplify each term

$x {}^{3} + 3x {}^{2} \frac{1}{x} + 3x( \frac{1}{x} ) {}^{2} + ( \frac{1}{x} ) {}^{3} \\ \\ = {x}^{3} + 3x + \frac{3}{x} + \frac{1}{x {}^{3} }$

Hence, ${x}^{3} + 3x + \frac{3}{x} + \frac{1}{x {}^{3} }$ is the solution.

Some useful identities:-

→ (a + b)^2 = a^2 + 2ab + b^2

→ (a – b)^2 = a^2 – 2ab + b^2

→ a^2 – b^2 = (a + b) (a – b)

→ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

→ (a + b – c)^2 = a^2 + b^2 + c^2 + 2ab – 2bc – 2ca

→ (a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca

→ (a + b)^3 = a^3 + b^3 + 3ab(a + b)

→ (a – b)^3 = a^3 – b^3 – 3ab(a – b)

→ (a^3 + b^3) = (a + b) (a^2 – ab + b^2)

→ (a^3 – b^3) = (a – b) (a^2 + ab + b^2)