Question

what is the formula of a³-b³​

Answer 1

a³-b³= (a-b)(a²+ab+ b²) is the formula.

• 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.”

let see the 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) +3ab]

➪a³-b³= (a-b)(a²+ab+ b²) [Proved]

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Answer 2

Answer:

a³-b³= (a-b)(a²+ab+ b²) is the formula.