a³-b³= its a formula please answer
Answers
Answer:
a³-b³= (a-b)(a²+ab+ b²)
Step-by-step explanation:
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]
Step-by-step explanation:
a³ + b³ = (a + b)(a² – ab + b²)
you know that
(a + b)³ = a³ + 3ab(a + b) + b³
then a³ + b³ = (a + b)³ – 3ab(a + b)
= (a + b)[(a + b)² – 3ab]
= (a + b)(a² + 2ab + b² – 3ab)
= (a + b)(a² – ab + b² )
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