Expand the Trigonometric Expression (x^2+y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Multiply $y$ by $y$ .

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

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

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

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

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

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