Question

(a - b)3 = a' – b3 – 3 ab (a - b)​

Answer 1

Answer:

(a-b)³ = a³-b³-3ab(a-b)

Step-by-step explanation:

(a-b)³ = (a-b)(a-b)²

= (a-b)(a²-2ab+b²)

= a(a²-2ab+b²)-b(a²-2ab+b²)

= a³-2a²b+ab²-a²b+2ab²-b³

= a³-3a²b+3ab²-b³

= a³-b³ -3a²b+3ab²

= a³-b³-3ab(a-b)

Therefore,

(a-b)³ = a³-b³-3ab(a-b)

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Answer 2

(a - b)³ = a³ – b³ – 3 ab (a - b)​

Step-by-step explanation:

(a - b)³ = a³ – b³ – 3 ab (a - b)​

To prove: L.H.S. = R.H.S.

L.H.S. = (a - b)³

(a - b)  (a - b)  (a - b)

(a - b)  (a - b)²

Substituting the formula:  (a - b)² = (a² + b² - 2ab)

(a - b)  (a² + b² - 2ab)

(a² × a) - (a² ×  b) + (b² × a) - (b² × b) - (2ab × a ) + (2ab × b)

a³ - a²b + ab² - b³ - 2a²b + 2ab²

Grouping the same variables together:

a³ - b³ - a²b - 2a²b + ab² + 2ab²

a³ - b³ - 3a²b + 3ab²

Taking out -3ab as common:

a³ – b³ – 3 ab (a - b)​

∴ L.H.S. = R.H.S.

(a - b)³ = a³ – b³ – 3 ab (a - b)​

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