How do you expand #(3+m/3)^5#?

1 Answer
Aug 3, 2017

Answer:

See a solution process below:

Explanation:

Solution for this problem is below:

We can use Pascal's triangle to solve this problem.

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The triangle values for the exponent 5 are:

#color(red)(1)color(white)(.........)color(red)(5)color(white)(.........)color(red)(10)color(white)(.........)color(red)(10)color(white)(.........)color(red)(5)color(white)(.........)color(red)(1)#

Therefore #(color(blue)(3) + color(green)(m/3))^5# can be multiplied as:

#color(red)(1)(color(green)((m/3))^0 * color(blue)(3)^5) + color(red)(5)(color(green)((m/3))^1 * color(blue)(3)^4) + color(red)(10)(color(green)((m/3))^2 * color(blue)(3)^3) + color(red)(10)(color(green)((m/3))^3 * color(blue)(3)^2) + color(red)(5)(color(green)((m/3))^4 * color(blue)(3)^1) + color(red)(1)(color(green)((m/3))^5 * color(blue)(3)^0) =>#

#color(red)(1)(color(green)(1) * color(blue)(3)^5) + color(red)(5)(color(green)(m) * color(blue)(3)^3) + color(red)(10)(color(green)(m)^2 * color(blue)(3)^1) + color(red)(10)(color(green)(m)^3 * color(blue)(3)^-1) + color(red)(5)(color(green)(m)^4 * color(blue)(3)^-3) + color(red)(1)(color(green)(m)^5 * color(blue)(3)^-5) =>#

#color(red)(1)(color(green)(1) * color(blue)(243)) + color(red)(5)(color(green)(m) * color(blue)(27)) + color(red)(10)(color(green)(m)^2 * color(blue)(3)) + color(red)(10)(color(green)(m)^3 * color(blue)(1/3)) + color(red)(5)(color(green)(m)^4 * color(blue)(1/27)) + color(red)(1)(color(green)(m)^5 * color(blue)(1/243)) =>#

#243 + 135m + 30m^2 + 10/3m^3 + 5/27m^4 + 1/243m^5#

Or, in standard form:

#1/243m^5 + 5/27m^4 + 10/3m^3 + 30m^2 + 135m + 243#