Simplify (3x^2+y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ .

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

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

Move $y$ .

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

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

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