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

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

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Answer 1 · 2016-02-08T11:25:08

$27 x^{3} + 54 x^{2} + 36 x + 8$ $27x^3 + 54x^2 + 36x + 8$

Explanation:

From Pascal's Triangle

using row with coefficients : 1 3 3 1

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

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

${(3 x + 2)}^{3} = 1 . {(3 x)}^{3} . {(2)}^{0} + 3 . {(3 x)}^{2} . {(2)}^{1} + 3 . {(3 x)}^{1} . {(2)}^{2} + 1 . {(3 x)}^{0} . {(2)}^{3}$ $(3x + 2 )^3 = 1.(3x)^3.(2)^0 + 3.(3x)^2.(2)^1 + 3.(3x)^1.(2)^2 + 1.(3x)^0.(2)^3$

$= 1 . (27 x^{3}) .1 + 3 . (9 x^{2}) .2 + 3 . (3 x) .4 + 1.1 .8$ $= 1.(27x^3).1 + 3.(9x^2).2 + 3.(3x).4 + 1.1.8$

$= 27 x^{3} + 54 x^{2} + 36 x + 8$ $= 27x^3 + 54x^2 + 36x + 8$

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

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