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

1 Answer
LM
Jan 3, 2018

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

Related questions
See all questions in The Binomial Theorem
Impact of this question
2223 views around the world
You can reuse this answer
Creative Commons License