Question

Common term in a² - b² and a³ - b³ is ?

Answer 1

Answer:

a-b

Step-by-step explanation:

a²-b²= (a-b)(a+b)

a³-b³= (a-b)(a²+ab+b²)

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Answer 2

We know the well-known formula

(a-b)³=a³-3 a²b+3 ab²-b³

By transposition,

a³ - b³ = (a-b)³ + 3 a²b - 3 ab²

a³ - b³ = (a-b)³ +3 ab(a-b)

a³ - b³ = (a-b) [(a-b)² +3 ab]

a³ - b³ = (a-b) [(a-b)² +3 ab]

We all know (a - b)² = a² - 2 ab + b²

So

a³ - b³ = (a-b) [(a² - 2 ab + b²) +3 ab]

a³-b³= (a-b)(a²+ab+ b²) [Proved]