Question #59622

1 Answer
Jan 14, 2018

See below for application of Pascal's triangle

Explanation:

Pascal's Triangle (first 6 rows)

#"row "color(blue)0": "1#
#"row "color(blue)1": "1color(white)("xx")1#
#"row "color(blue)2": "1color(white)("xx")2color(white)("xx")1#
#"row "color(blue)3": "1color(white)("xx")3color(white)("xx")3color(white)("xx")1#
#"row "color(blue)4": "1color(white)("xx")4color(white)("xx")6color(white)("xx")4color(white)("xx")1#
#"row "color(blue)5": "1color(white)("xx")5color(white)("x")10color(white)("x")10color(white)("xx")5color(white)("xx")1#
#"row "color(red)6": "1color(white)("xx")6color(white)("x")15color(white)("x")20color(white)("x")15color(white)("xx")6color(white)("xx")1#

The #color(red)6"th"# row provides the coefficients for descending powers of #x# in the expansion of #(x+1)^color(red)6#
#color(white)("xxx")1x^6+6x^5+15x^4+20x^3+15x^2+ 6x+1#