Question

Derive the formulae of (a+b)³ and (a-b)³

Answer 1

Answer:

a^3+b^3=a^3+b^3+3ab(a+b)

similary a^3-b^3= a^3-b^3-3ab(a-b)

Step-by-step explanation:

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Answer 2

Answer:

• (a+b)³$= a^3 +3ab(a-b)+b^3$
• (a-b)³ $= a^3 - 3ab(a-b) - b^3$

Step-by-step explanation:

Derive the formulae of (a+b)³

$(a + b)^3 = (a+ b)(a +b)(a + b)\\ = (a^2 + 2ab + b^2)(a + b) \\= a^3 + a^2b + 2a^2b + 2ab^2 + ab^2 +b^3 \\ = a^3 + 3a^2b + 3ab^2 + b^3 \\ = a^3 +3ab(a-b)+b^3$

Derive the formulae of (a-b)³

$(a - b)^3 = (a - b)(a - b)(a - b)\\ = (a^2 - 2ab + b^2)(a - b) \\= a^3 - a^2b - 2a^2b + 2ab^2 + ab^2 - b^3 \\= a^3 - 3a^2b + 3ab^2 - b^3 \\= a^3 - 3ab(a-b) - b^3$