Question #f79cd

1 Answer
Oct 11, 2017

See below

Explanation:

I assume you want this expanded.

#(2x+y)^10#

Using the Binomial Theorem.

#2^10color(white)(.) 10 C 10color(white)(.)x^10y^0+2^9 color(white)(.)10C9color(white)(.) x^9y+2^8color(white)(.) 10C8color(white)(.)x^8y^2+2^7color(white)(.) 10C7color(white)(.)x^7y^3+2^6color(white)(.) 10C6color(white)(.)x^6y^4+2^5color(white)(.) 10C5color(white)(.)x^5y^5+2^4color(white)(.) 10C4color(white)(.)x^4y^6+2^3color(white)(.) 10C3color(white)(.)x^3y^7+2^2color(white)(.) 10c2color(white)(.)x^2y^8+2^1color(white)(.) 10C1color(white)(.)x^1y^9+2^0color(white)(.)10C0color(white)(.)x^0y^10#

#->2^10* 1*x^10y^0+2^9 *10*x^9y+2^8* 45*x^8y^2+2^7*120*x^7y^3+2^6*210*x^6y^4+2^5* 252*x^5y^5+2^4*210*x^4y^6+2^3* 120*x^3y^7+2^2* 45*x^2y^8+2^1*10*x^1y^9+2^0*1*x^0y^10#

#->color(blue)(1024x^10+5120x^9y+11520 x^8y^2+15360x^7y^3+13440x^6y^4+8064x^5y^5+3360x^4y^6+960x^3y^7+180x^2y^8+20x^1y^9+y^10)#