How do you use the binomial theorem to expand and simplify the expression #(r+3s)^6#?

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Answer 1 · 2018-01-29T09:36:24

#color(green)((r + 3s)^6 = r^6 +18r^5s + 135r^4s^2 + 540r^3s^3 + 1215r^2s^4 + 1458rs^5 + 729)#

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As per Pascal's Triangle coefficients of the terms are

1 6 15 20 15 6 1

#(r + 3s)^6 = r^6 + 6 r^5(3s) + 15 r^4 (3s)^2 + 20 r^3 (3s)^3 + 15 r^2 (3s)^4 + 6 r (3s)^5 + (3s)^6#

#color(green)((r + 3s)^6 = r^6 +18r^5s + 135r^4s^2 + 540r^3s^3 + 1215r^2s^4 + 1458rs^5 + 729)#