Find the Product 4x^2(3x^2+1)

$4 x^{2} (3 x^{2} + 1)$

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $1$ .

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

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $4$ by $3$ .

$12 x^{4} + 4 x^{2}$