Question

Expand the following binomial:
${(1-xy)}^7$

Answer 1

${(x+y)}^n$

$\Rightarrow \sum _{r=0}^n{}_r^{n}C{x}^{n-r}{y}^r$

for the given expression

$={}_0^{7}C{(-xy)}^0+{}_1^7{C{(-xy)}^1+}_2^{7}C{(-xy)}^2{+}_3^7{C{(-xy)}^3+}_4^{7}C{(-xy)}^4{+}_5^7{(-xy)}^5{+}_6^7{(-xy)}^6{+}_7^7{(-xy)}^7$

$=1-7xy+21x^2{y}^2-35x^3{y}^3+35x^4{y}^4-21x^5{y}^5+7x^6{y}^6-x^7{y}^7$