Define the formula of $a^{3} - b^{3}$

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Solution

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
For example $(2^{3} - 1^{3}) = (2 - 1) (4 + 2 \times 1 + 1) (2^{3} - 1^{3}) = 7$

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a^{3} - b^{3}

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Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

Prove the following identities :

$(i) {(a + b)}^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 b^{2} a$

$(i i) {(a - b)}^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 b^{2} a$ [4 MARKS]

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