Find the Product (1+3x^2)^2

${(1 + 3 x^{2})}^{2}$

Step 1

Rewrite ${(1 + 3 x^{2})}^{2}$ as $(1 + 3 x^{2}) (1 + 3 x^{2})$ .

$(1 + 3 x^{2}) (1 + 3 x^{2})$

Step 2

Expand $(1 + 3 x^{2}) (1 + 3 x^{2})$ using the FOIL Method.

Apply the distributive property.

$1 (1 + 3 x^{2}) + 3 x^{2} (1 + 3 x^{2})$

Apply the distributive property.

$1 \cdot 1 + 1 (3 x^{2}) + 3 x^{2} (1 + 3 x^{2})$

Apply the distributive property.

$1 \cdot 1 + 1 (3 x^{2}) + 3 x^{2} \cdot 1 + 3 x^{2} (3 x^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (3 x^{2}) + 3 x^{2} \cdot 1 + 3 x^{2} (3 x^{2})$

Multiply $3 x^{2}$ by $1$ .

$1 + 3 x^{2} + 3 x^{2} \cdot 1 + 3 x^{2} (3 x^{2})$

Multiply $3$ by $1$ .

$1 + 3 x^{2} + 3 x^{2} + 3 x^{2} (3 x^{2})$

Rewrite using the commutative property of multiplication.

$1 + 3 x^{2} + 3 x^{2} + 3 \cdot 3 x^{2} x^{2}$

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

Move $x^{2}$ .

$1 + 3 x^{2} + 3 x^{2} + 3 \cdot 3 (x^{2} x^{2})$

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

$1 + 3 x^{2} + 3 x^{2} + 3 \cdot 3 x^{2 + 2}$

Add $2$ and $2$ .

$1 + 3 x^{2} + 3 x^{2} + 3 \cdot 3 x^{4}$

Multiply $3$ by $3$ .

$1 + 3 x^{2} + 3 x^{2} + 9 x^{4}$

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

$1 + 6 x^{2} + 9 x^{4}$