Answer:
[tex]x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7[/tex]
Step-by-step explanation:
Given: equation =[tex](x + 2y)^7[/tex]
Using binomial expansion which state that
[tex](a+b)^n=\sum {_{n}\textrm{C}_k a^{n-k}b^k}[/tex]
where a= x, b=2y, n=(0,1,2...,7), k =(0,1,2....,7)
Applying the binomial expansion
We get,
[tex]\frac{7!}{(7-0)!0!} x^{7-0}(2y)^0+ \frac{7!}{(7-1)!1!} x^{7-1}(2y)^1+\frac{7!}{(7-2)!2!} x^{7-2}(2y)^2+\frac{7!}{(7-3)!3!} x^{7-3}(2y)^3+ \frac{7!}{(7-4)!4!} x^{7-4}(2y)^4+\frac{7!}{(7-5)!5!} x^{7-5}(2y)^5+\frac{7!}{(7-6)!6!} x^{7-6}(2y)^6+ \frac{7!}{(7-7)!7!} x^{7-7}(2y)^7[/tex]
solving this we get,
[tex]x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7[/tex]
