Verify: (a - b) (a - b) (a - b) = a³ - 3a²b + 3ab² - b³

Solution:

Given, (a - b) (a - b) (a - b) = a³ - 3a²b + 3ab² - b³

L.H.S = (a - b) (a - b) (a - b)

= (a² - 2ab + b²) (a - b)

= a³ - a²b - 2a²b + 2ab² + ab² - b³

= a³ - 3a²b + 3ab² - b³

= R.H.S

L.H.S. = R.H.S.

✦ Try This: Verify: (2p - 3q)(2p - 3q)(2p - 3q) = 8p³ - 36p²q + 54pq² - 27q³

Given, (2p - 3q)(2p - 3q)(2p - 3q) = 8p³ - 36p²q + 54pq² - 27q³

L.H.S. = (2p - 3q)(2p - 3q)(2p - 3q)

= [(2p)² - 2(2p)(3q) + (3q)²]

= (4p² - 12pq + 9q²)(2p - 3q)

= 8p³ - 12p²q - 24p²q + 36pq² + 18pq² - 27q³

= 8p³ - 36p²q + 54pq² - 27q³

= R.H.S.

L.H.S. = R.H.S.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 113(vi)

Verify: (a - b) (a - b) (a - b) = a³ - 3a²b + 3ab² - b³

Summary:

(a - b) (a - b) (a - b) = a³ - 3a²b + 3ab² - b³ is true

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