Question

The binomial expansion of (x + y^2)^2 is

Answer 1

Express this as two expressions:

`(x+y^2)(x+y^2)`
Distribute,

`x^2 + xy^2 + xy^2 + y^4`
And now simplify:

`x^2 + 2xy^2 + y^4`

Answer 2

`x^(2)+y^(4)+2xy^(2)`

Explanation:

The given expression is (x + y²)² and we have to simplify it to find the binomial expansion.

(x + y²)² is in the form of (a + b)².

When we expand (a + b)² we get the binomial expression

(a + b)² = a² + b² + 2ab

Now we put the value of a = x and b = y²

(x + y²)² = x² + (y²)² + 2(x)(y²)

=
`x^(2)+y^(4)+2xy^(2)`

Therefore answer is
`x^(2)+y^(4)+2xy^(2)`