How do you expand #(x+3)^5#?

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Answer 1 · 2017-05-09T15:14:01

#x^5+15x^4+90x^3+270x^2+405x+243#

The simplest way is by Pascals triangle

the coefficients for expansions are found by :

#1#
#(x+y)^2rarr" "1,2,1#
#(x+y)^3rarr" "1,3,3,1#
#(x+y)^4rarr" "1,4,6,4,1#
#color(blue)((x+y)^5rarr" "1,5,10,10,5,1)#

etc....

the powers for#(x+y)^5#

will be#rarr x^5, x^4y, x^3y^2 x^2y^3, xy^4,y^5#

so putting the two together we have:

#(x+3)^5#
#=color(blue)(1)x^5+color(blue)(5)x^4 *3+color(blue)(10)x^3*3^2+color(blue)(10)x^2*3^3+color(blue)(5)x*3^4+ color(blue)(1)* 3^5#

#=x^5+15x^4+90x^3+270x^2+405x+243#