Question

Verify : (i) x ³ + y ³ = (x + y) (x ² – xy + y ² ) (ii) x ³ – y ³ = (x – y) (x ² + xy + y ² ).

Answer 1

(i) It is known that, 

(x + y)³ = x³ + y³ + 3xy(x + y)

x³ + y³ = (x + y)³ - 3xy (x + y) 

= (x + y) [(x + y)² - 3xy] 

= (x + y) (x² + y² + 2xy - 3xy) 

= (x + y) (x² + y² - xy) 

= (x + y) (x² - xy + y2)

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(ii) It is known that, 

(x - y)³ = x³ - y³ - 3xy (x - y)

x³ - y³ = (x - y)³ + 3xy (x - y) 

= (x - y) [(x - y)² + 3xy] 

= (x - y) (x² + y² - 2xy + 3xy) 

= (x - y) (x² + y² + xy) 

= (x - y) (x² + xy + y²).