How do you use the binomial series to expand $(x + 3)^6$ ?

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Answer 1 · 2017-05-14T15:12:09

$x^6 + 18x^5 + 135x^4 + 540x^3 + 1215x^2 + 1458x +729$

The binomial series gives you :
$(a+b)^6 = a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 +b^6$

Substitute a and b by x and 3 and you get:

$(x+3)^6 = x^6 + 18x^5 + 135x^4 + 540x^3 + 1215x^2 + 1458x +729$

How do you use the binomial series to expand (x + 3)^6 (x + 3)^6?