Simplify (x^2+y)(x+y^2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Simplify each term.

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + x^{2} y^{2} + y x + y \cdot y^{2}$

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

$x^{2 + 1} + x^{2} y^{2} + y x + y \cdot y^{2}$

Add $2$ and $1$ .

$x^{3} + x^{2} y^{2} + y x + y \cdot y^{2}$

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

Multiply $y$ by $y^{2}$ .

Raise $y$ to the power of $1$ .

$x^{3} + x^{2} y^{2} + y x + y^{1} y^{2}$

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

$x^{3} + x^{2} y^{2} + y x + y^{1 + 2}$

Add $1$ and $2$ .

$x^{3} + x^{2} y^{2} + y x + y^{3}$

Simplify the expression.

Reorder $y$ and $x$ .

$x^{3} + x^{2} y^{2} + x y + y^{3}$

Move $x y$ .

$x^{3} + x^{2} y^{2} + y^{3} + x y$

Reorder $x^{3}$ and $x^{2} y^{2}$ .

$x^{2} y^{2} + x^{3} + y^{3} + x y$