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Mathematics

(a3 - b3) ÷ (a - b) is equal to :

  1. a2 + b2 + ab

  2. a2 + b2 - ab

  3. a2 - b2 + ab

  4. a2 - b2 - ab

Algebraic Expressions

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Answer

(a3 - b3) ÷ (a - b)

[∵ As we know, (x3 - y3) = (x - y)(x2 + y2 + xy)]

∴ (a3 - b3) ÷ (a - b) = (a−b)(a2+b2+ab)(a−b)\dfrac{(a - b)(a^2 + b^2 + ab)}{(a - b)}

= (a−b)(a2+b2+ab)(a−b)\dfrac{\cancel{(a - b)}(a^2 + b^2 + ab)}{\cancel{(a - b)}}

= (a2 + b2 + ab)

Hence, option 1 is the correct option.

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