A CUBE MINUS B CUBE FORMULA

     

(a³ + b³) = (a + b)³ – 3ab(a + b)…………………………….(2)

Take the common term, then we get

(a³ + b³) = (a + b) <(a + b)2 – 3ab>…………………………..(3)

We know that

(a + b)2 = a² + 2ab + b²……………………….(4)

Substitute the equation (4) in equation (3).

(a³ + b³) = (a + b) <(a² + 2ab + b²) – 3ab>………………(5)

(a³ + b³) = (a + b)(a² – ab + b²)

Let us prove the above equation.

Consider a = 2 and b = 3. Substitute the value of a và b in the equation (5)

(23 + 33) = (2 + 3)(22 – 2✕3 + 32)

Consider LHS first

LHS = (23 + 33)

LHS = (8 + 27)

LHS = 35

Let us consider the RHS

RHS = (2 + 3)(22 – 2✕3 + 33)

RHS = (5)(4 – 6 + 9)

RHS = (5)(7)

RHS = 35

∴ LHS = RHS

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