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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

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

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

Add $3$ and $3$ .

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

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

Move $y^{3}$ .

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

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

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

Step 4

Move $4 x^{4}$ .

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

Step 5

Reorder $4 x^{2} y^{3}$ and $y^{6}$ .

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