Find the Product (x^3+3)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{3} x^{3} + x^{3} \cdot 3 + 3 x^{3} + 3 \cdot 3$

Step 3

Simplify and combine like terms.

Simplify each term.

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

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

$x^{3 + 3} + x^{3} \cdot 3 + 3 x^{3} + 3 \cdot 3$

Add $3$ and $3$ .

$x^{6} + x^{3} \cdot 3 + 3 x^{3} + 3 \cdot 3$

Move $3$ to the left of $x^{3}$ .

$x^{6} + 3 \cdot x^{3} + 3 x^{3} + 3 \cdot 3$

Multiply $3$ by $3$ .

$x^{6} + 3 x^{3} + 3 x^{3} + 9$

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

$x^{6} + 6 x^{3} + 9$