Simplify (x+y^2)^2

${(x + y^{2})}^{2}$

Step 1

Rewrite ${(x + y^{2})}^{2}$ as $(x + y^{2}) (x + y^{2})$ .

$(x + y^{2}) (x + y^{2})$

Step 2

Expand $(x + y^{2}) (x + y^{2})$ using the FOIL Method.

Apply the distributive property.

$x (x + y^{2}) + y^{2} (x + y^{2})$

Apply the distributive property.

$x \cdot x + x y^{2} + y^{2} (x + y^{2})$

Apply the distributive property.

$x \cdot x + x y^{2} + y^{2} x + y^{2} y^{2}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x y^{2} + y^{2} x + y^{2} y^{2}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} + x y^{2} + y^{2} x + y^{2 + 2}$

Add $2$ and $2$ .

$x^{2} + x y^{2} + y^{2} x + y^{4}$

Add $x y^{2}$ and $y^{2} x$ .

Reorder $y^{2}$ and $x$ .

$x^{2} + x y^{2} + x y^{2} + y^{4}$

Add $x y^{2}$ and $x y^{2}$ .

$x^{2} + 2 x y^{2} + y^{4}$

Step 4

Move $x^{2}$ .

$2 x y^{2} + y^{4} + x^{2}$

Step 5

Reorder $2 x y^{2}$ and $y^{4}$ .

$y^{4} + 2 x y^{2} + x^{2}$