Question

Plz solve this question...​

Answer 1

Answer:
`x^(10)+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5`

Explanation:

`\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _(i=0)^n\binom{n}{i}a^(\left(n-i\right))b^i`

`a=x^2,\:\:b=2y`

`=\sum _(i=0)^5\binom{5}{i}\left(x^2\right)^(\left(5-i\right))\left(2y\right)^i`
`=(5!)/(0!\left(5-0\right)!)\left(x^2\right)^5\left(2y\right)^0+(5!)/(1!\left(5-1\right)!)\left(x^2\right)^4\left(2y\right)^1+(5!)/(2!\left(5-2\right)!)\left(x^2\right)^3\left(2y\right)^2+(5!)/(3!\left(5-3\right)!)\left(x^2\right)^2\left(2y\right)^3+(5!)/(4!\left(5-4\right)!)\left(x^2\right)^1\left(2y\right)^4+(5!)/(5!\left(5-5\right)!)\left(x^2\right)^0\left(2y\right)^5`

simplify all =
`x^(10)+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5`