How do you expand (3x+2)^3(3x+2)3 using Pascal’s Triangle?

1 Answer
Jim G.
Feb 8, 2016

27x^3 + 54x^2 + 36x + 827x3+54x2+36x+8

Explanation:

From Pascal's Triangle

using row with coefficients : 1 3 3 1

with decreasing powers of 3x from (3x)^3 color(black)(" to ") (3x)^0(3x)3 to (3x)0

and increasing powers of 2 from (2)^0color(black)(" to ") (2)^3(2)0 to (2)3

(3x + 2 )^3 = 1.(3x)^3.(2)^0 + 3.(3x)^2.(2)^1 + 3.(3x)^1.(2)^2 + 1.(3x)^0.(2)^3 (3x+2)3=1.(3x)3.(2)0+3.(3x)2.(2)1+3.(3x)1.(2)2+1.(3x)0.(2)3

= 1.(27x^3).1 + 3.(9x^2).2 + 3.(3x).4 + 1.1.8 =1.(27x3).1+3.(9x2).2+3.(3x).4+1.1.8

= 27x^3 + 54x^2 + 36x + 8 =27x3+54x2+36x+8

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