Simplify (3-x^2)(x^2-4)

$(3 - x^{2}) (x^{2} - 4)$

Expand $(3 - x^{2}) (x^{2} - 4)$ using the FOIL Method.

Apply the distributive property.

$3 (x^{2} - 4) - x^{2} (x^{2} - 4)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 4$ .

$3 x^{2} - 12 - x^{2} x^{2} - x^{2} \cdot - 4$

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

Move $x^{2}$ .

$3 x^{2} - 12 - (x^{2} x^{2}) - x^{2} \cdot - 4$

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

$3 x^{2} - 12 - x^{2 + 2} - x^{2} \cdot - 4$

Add $2$ and $2$ .

$3 x^{2} - 12 - x^{4} - x^{2} \cdot - 4$

Multiply $- 4$ by $- 1$ .

$3 x^{2} - 12 - x^{4} + 4 x^{2}$

Add $3 x^{2}$ and $4 x^{2}$ .

$7 x^{2} - 12 - x^{4}$

Move $- 12$ .

$7 x^{2} - x^{4} - 12$

Reorder $7 x^{2}$ and $- x^{4}$ .

$- x^{4} + 7 x^{2} - 12$