What is the rule for cubing a binomial?

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Answer 1 · 2015-10-26T23:00:29

#(a+b)^3 = a^3+3a^2b+3ab^2+b^3#

The coefficients #1, 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#

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

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

#(2x-5)^3#

#= (a+b)^3 = a^3+3a^2b+3ab^2+b^3#

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

#=8x^3-60x^2+150x-125#