Prove:
$(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ .

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Solution

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

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

$= a^{3} + 2 a^{2} b + a b^{2} + a^{2} b + 2 a b^{2} + b^{3}$

$= a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$

Hence Proved.

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Similar questions

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

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - 8

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