Simplify (2x^3+y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

$2 \cdot 2 x^{6} + 2 x^{3} y + y (2 x^{3}) + y \cdot y$

Multiply $2$ by $2$ .

$4 x^{6} + 2 x^{3} y + y (2 x^{3}) + y \cdot y$

Rewrite using the commutative property of multiplication.

$4 x^{6} + 2 x^{3} y + 2 y x^{3} + y \cdot y$

Multiply $y$ by $y$ .

$4 x^{6} + 2 x^{3} y + 2 y x^{3} + y^{2}$

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

Move $y$ .

$4 x^{6} + 2 x^{3} y + 2 x^{3} y + y^{2}$

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

$4 x^{6} + 4 x^{3} y + y^{2}$