(a+b)^3=(a+b)(a+b)(a+b) #160; #160; #160; #160; #160; #160; #160; #160; =[a(a+b)+b(a+b)](a+b) #160; #160; #160; #16 ...

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Terms

Expand a+b3

Question

Expand $(a + b)^{3}$

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Solution

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

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