How do you use the binomial series to expand #(a + 3b^3)^5#?

1 Answer
Jan 29, 2018

Answer:

#color(purple)((a + 3b^3)^5 = a^5 +15a^4b^3 + 90a^3b^6 + 270a^2b^9 + 405ab^12 + 243b^15)#

Explanation:

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Using Pascal's Triangle to get the coefficients for power 5

1 5 10 10 5 1

#(a + 3b^3)^5 = a^5 + 5 a^4 (3b^3) + 10 a^3 (3b^3)^2 + 10 a^2 (3b^3)^3 + 5 a (3b^3)^4 + (3b^3)^5#

#color(purple)((a + 3b^3)^5 = a^5 +15a^4b^3 + 90a^3b^6 + 270a^2b^9 + 405ab^12 + 243b^15)#