Simplify (4x^2+y)^2

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

Rewrite ${(4 x^{2} + y)}^{2}$ as $(4 x^{2} + y) (4 x^{2} + y)$ .

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

Expand $(4 x^{2} + y) (4 x^{2} + y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $4$ by $4$ .

$16 x^{4} + 4 x^{2} y + y (4 x^{2}) + y \cdot y$

Rewrite using the commutative property of multiplication.

$16 x^{4} + 4 x^{2} y + 4 y x^{2} + y \cdot y$

Multiply $y$ by $y$ .

$16 x^{4} + 4 x^{2} y + 4 y x^{2} + y^{2}$

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

Move $y$ .

$16 x^{4} + 4 x^{2} y + 4 x^{2} y + y^{2}$

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

$16 x^{4} + 8 x^{2} y + y^{2}$