What is the formula for $(a+b)^3$ ?

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Answer 1 · 2015-02-03T17:49:14

The answer is: $(a+b)^3=a^3+3a^2b+3ab^2+b^3$ .

It's easy to prove:

$(a+b)^3=$
$=(a+b)(a+b)(a+b)=$
$=(a^2+ab+ab+b^2)(a+b)=$
$=(a^2+2ab+b^2)(a+b)=$
$=a^3+a^2b+2a^2b+2ab^2+ab^2+b^3=$
$=a^3+3a^2b+3ab^2+b^3$ .

What is the formula for (a+b)^3(a+b)^3?