Question

(x-1/x) ( x^2+1+1/x^2)
simplify using identity​

Answer 1

Given

(x-1/x) ( x^2+1+1/x^2)

simplify using identity

Solution

★ Applying identity :

a³ - b³ = (a - b)(a² + ab + b²)

→ (x-1/x) ( x²+1+1/x²)

→ (x - 1/x) [(x)² + x*1/x + (1/x)²]

→ x³ - 1/x³

Some identities

• (a+b)² = a² + b² +2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ -b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ + b³ = (a+b)(a² - ab +b²)
• a³ - b³ = (a-b)(a² + ab + b²)