How do you multiply #(x+7)^4#?

1 Answer
Alan P.
Aug 8, 2015

#x^4 + 28x^3 + 294x^2 + 1372x + 2401#

Explanation:

Using the first 5 rows of Pascal's Triangle:
#{: (0, ":", 1,,,,), (1, ":", 1, 1,,,), (2,":", 1,2, 1,,), (3,":",1,3,3,1,), (4,":",1,4,6,4,1) :}#

#(a+b)^4 = 1a^4b^0+4a^3b^1+6a^2b^2+4a^1b^3+1a^0b^4#

Substituting #x# for #a# and #7# for #b#

#(x+7)^4#
#color(white)("XXXX")##= x^4 + 4x^3(7^1)+6x^2(7^2)+4x(7^3) + 1(7^4)#

#color(white)("XXXX")##=x^4 + 28x^3 + 294x^2 + 1372x + 2401#

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