What is the rule for cubing a binomial?

1 Answer
Oct 26, 2015

(a+b)^3 = a^3+3a^2b+3ab^2+b^3(a+b)3=a3+3a2b+3ab2+b3

Explanation:

The coefficients 1, 3, 3, 11,3,3,1 can be found as a row of Pascal's triangle:

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For other powers of a binomial use a different row of Pascal's triangle.

For example:

(a+b)^5 = a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5(a+b)5=a5+5a4b+10a3b2+10a2b3+5ab4+b5

How about (2x-5)^3(2x5)3 or similar?

Let a=2xa=2x and b=-5b=5 to find:

(2x-5)^3(2x5)3

= (a+b)^3 = a^3+3a^2b+3ab^2+b^3=(a+b)3=a3+3a2b+3ab2+b3

=(2x)^3+3(2x)^2(-5)+3(2x)(-5)^2+(-5)^3=(2x)3+3(2x)2(5)+3(2x)(5)2+(5)3

=8x^3-60x^2+150x-125=8x360x2+150x125