How do you use the binomial theorem to expand and simplify the expression #(1/x+y)^5#?

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Answer 1 · 2018-01-29T02:50:49

#color(red)((1/x+ y)^5 =1/x^5 +( 5y)/x^4 + (10y^2)/x^3 + (10 y^3)/x^2 + (5 y^4)/x + y^5)#

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As per Pascal's 5th row, constant coefficients of the 6 terms are

1 5 10 10 5 1

#(1/x+ y)^5 = (1 * (1/x)^5 y^0 + 5 * (1/x)^4 y + 10 * (1/x)^3 y^2 + 10 * (1/x2) y^3 + 5 * (1/x) * y^4 + 1 * (1/x)^0 * y^5)#

#(1/x+ y)^5 = x^-5 + 5 x^-4 y + 10 x^-3 y^2 + 10 x_-2 y^3 + 5 x^-1 y^4 + y^)#

#color(red)((1/x+ y)^5 =1/x^5 +( 5y)/x^4 + (10y^2)/x^3 + (10 y^3)/x^2 + (5 y^4)/x + y^5)#