How do you use the binomial theorem to expand and simplify the expression #(c+d)^3#?

1 Answer
Jan 3, 2018

Answer:

#c^3 + 3c^2d + 3cd^2 + d^3#

Explanation:

1 #(c+d)^0#
1 1 #(c+d)^1#
1 2 1 #(c+d)^2#
1 3 3 1 #(c+d)^3#

#(c+d)^0 = 1#
#(c+d)^1 = 1(c) + 1(d)#
#(c+d)^2 = 1(c^2)(d^0) + 2(c^1)(d^1) + 1(c^0)(d^2)#
#(c+d)^3 = 1(c^3)(d^0) + 3(c^2)(d^1) + 3(c^1)(d^2) + 1(c^0)(d^3)#

#(c+d)^0 = 1#
#(c+d)^1 = c + d#
#(c+d)^2 = 1(c^2)cancel((d^0)) + 2(c^1)(d^1) + 1cancel((c^0))(d^2)#
#(c+d)^3 = 1(c^3)cancel((d^0)) + 3(c^2)(d^1) + 3(c^1)(d^2) + 1cancel((c^0))(d^3)#

#(c+d)^0 = 1#
#(c+d)^1 = c+d#
#(c+d)^2 = c^2 + 2cd + d^2#
#(c+d)^3 = c^3 + 3c^2d + 3cd^2 + d^3#