How do you expand #(x+4)^4#?

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Answer 1 · 2015-12-19T13:55:32

#x^4+16x^3+96x^2+256x+256#

The fourth row of Pascal's triangle is

#1,4,6,4,1#

Therefore,

#(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4#

This can be applied as follows:

#(x+4)^4=(x)^4+4(x)^3(4)+6(x)^2(4)^2+4(x)(4)^3+(4)^4#

#=x^4+16x^3+96x^2+256x+256#