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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

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

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

Add $3$ and $3$ .

$9 x^{4} + 3 x^{2} y^{3} + 3 y^{3} x^{2} + y^{6}$

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

Move $y^{3}$ .

$9 x^{4} + 3 x^{2} y^{3} + 3 x^{2} y^{3} + y^{6}$

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

$9 x^{4} + 6 x^{2} y^{3} + y^{6}$

Step 4

Move $9 x^{4}$ .

$6 x^{2} y^{3} + y^{6} + 9 x^{4}$

Step 5

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

$y^{6} + 6 x^{2} y^{3} + 9 x^{4}$