Question

Verify :

x^{​​​​​​3} + y^{​​​​​​3} = (x + y) (x^{​​​​​​2} + y^{​​​​​​2} – xy)

Answer 1

Q). Verify that x³ + y³ = (x+y) ( x² - xy + y²)

1). R.H.S => (x+y) ( x² - xy + y²)
=> x³ - x²y + xy² + x²y - xy² + y³ {On multiplying x³ + y³ with (x+y) ( x2 - xy + y²)}
=> [x³ + y³] + ( -x²y + x²y) + ( xy² - xy²)
=> x³ + y³
Since R.H.S = L.H.S,
That is x³ + y³ = x³ + y³
Hence, verified that x³ + y³ = (x+y) ( x² - xy + y²)

OR
2). L.H.S => Using identities.. (a³ + b³) = (a+b)(a2 - ab +b2)
=> (x+y) [(x)² - ( x * y ) + (y)²]
=> (x+y) ( x² - xy + y²)
Since, L.H.S = R.H.S,
that is (x+y) ( x² - xy + y²) = (x+y) ( x² - xy + y²)
Hence verified that x³ + y³ = (x+y) ( x² - xy + y²)

Although, for verifying the first step is mostly used !