Question

alternative formula of 8m³+b³​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

a³-b³= (a-b)(a²+ab+ b²)

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.”

Proff:

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]