Question

prove that: X³+ Y³ = (X + Y)(X² - XY + Y²)

Answer 1

x³ + y³ = (x + y) (x² - xy + y²)

_________ [GIVEN]

$\bold{Method\:1)}$

• Take L.H.S.

=> x³ + y³ = (x + y)³ - 3xy (x + y)

» Take (x + y) common

=> (x + y) [(x + y)² - 3xy (1)]

=> (x + y) [(x² + 2xy + y²) - 3xy]

Because (a + b)² = a² + 2ab + b²

=> (x + y) (x² + y² + 2xy - 3xy)

=> (x + y) (x² + y² - xy)

• L.H.S. = R.H.S.

___________ [HENCE PROVED]

$\bold{Method\:2)}$

• Take R.H.S.

=> (x + y) (x² - xy + y²)

=> x(x² - xy + y²) + y(x² - xy + y²)

=> x³ - x²y +xy² + x²y - xy² + y³

=> x³ + y³

• L.H.S. = R.H.S.

___________ [HENCE PROVED]

Answer 2

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Step-by-step explanation:

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