Simplify (3x^2+y^2)^2

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

Rewrite ${(3 x^{2} + y^{2})}^{2}$ as $(3 x^{2} + y^{2}) (3 x^{2} + y^{2})$ .

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

Expand $(3 x^{2} + y^{2}) (3 x^{2} + y^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$3 \cdot 3 x^{4} + 3 x^{2} y^{2} + y^{2} (3 x^{2}) + y^{2} y^{2}$

Multiply $3$ by $3$ .

$9 x^{4} + 3 x^{2} y^{2} + y^{2} (3 x^{2}) + y^{2} y^{2}$

Rewrite using the commutative property of multiplication.

$9 x^{4} + 3 x^{2} y^{2} + 3 y^{2} x^{2} + y^{2} y^{2}$

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

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

$9 x^{4} + 3 x^{2} y^{2} + 3 y^{2} x^{2} + y^{2 + 2}$

Add $2$ and $2$ .

$9 x^{4} + 3 x^{2} y^{2} + 3 y^{2} x^{2} + y^{4}$

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

Move $y^{2}$ .

$9 x^{4} + 3 x^{2} y^{2} + 3 x^{2} y^{2} + y^{4}$

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

$9 x^{4} + 6 x^{2} y^{2} + y^{4}$