can u prove a³+b³=(a+b)(a²+b²-ab)
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Answered by
2
Answer:
by using identity of polynomials we can prove it
Answered by
3
Step-by-step explanation:
(a+b)³
= (a+b)²(a+b)
= (a² + b² + 2ab)(a + b)
= a³ + ab² + 2a²b + a²b + b³ + 2ab²
= a³ + b³ + 3a²b + 3ab²
= a³ + b³ + 3ab(a + b)
Therefore,
(a + b)³ = a³ + b³ + 3ab(a + b)
We know,
(a + b)³ = a³ + b³ + 3ab(a + b)
a³ + b³ = (a + b)³ - 3ab(a + b)
a³ + b³ = (a + b)[(a + b)² - 3ab]
a³ + b³ = (a + b)[a² + b² + 2ab - 3ab]
a³ + b³ = (a + b)(a² + b² - ab)
Hence proved.
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