What is expanded from of a³-b³
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Answer:What is the formula of a³- b³?
Answer:What is the formula of a³- b³?Answer: a³-b³= (a-b)(a²+ab+ b²)
Step-by-step explanation:
Expressed in words, the difference of the cubes of two quantities is the product of the difference of the two quantities by the “imperfect square of the sum.”
Proof:
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]
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Answer:
a³ - b³ = (a - b)(a² + ab + b²)
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