Verify: i) x³ + y³ = (x + y)(x² - xy + y²)
ii) x³ - y³ = (x - y)(x² + xy + y²)

Solution:

i) x³ + y³ = (x + y)(x² - xy + y² )

Taking the RHS,

(x + y)(x² - xy + y²) = x(x² - xy + y² ) + y(x² - xy + y²)

= x³ - x²y + xy² + x²y - xy² + y³

= x³ + y³ = LHS

ii) x³ - y³ = (x - y)(x² + xy + y²)

Taking the RHS,

(x - y)(x² + xy + y²) = x (x² + xy + y²) - y (x² + xy + y²)

= x³ + x²y + xy² - x²y - xy² - y³

= x³ - y³ = LHS

Hence, verified.

☛ Check: Class 9 Maths NCERT Solutions Chapter 2

Video Solution:

Verify: i) x³ + y³ = (x + y)(x² - xy + y²) ii) x³ - y³ = (x - y)(x² + xy + y²)

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 9

Summary:

Hence, verified x³ + y³ = (x + y)(x² − xy + y²) and x³ − y³ = (x − y)(x² + xy + y²).

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