Simplify (2-x^2)(x^2-9)

$(2 - x^{2}) (x^{2} - 9)$

Step 1

Expand $(2 - x^{2}) (x^{2} - 9)$ using the FOIL Method.

Apply the distributive property.

$2 (x^{2} - 9) - x^{2} (x^{2} - 9)$

Apply the distributive property.

$2 x^{2} + 2 \cdot - 9 - x^{2} (x^{2} - 9)$

Apply the distributive property.

$2 x^{2} + 2 \cdot - 9 - x^{2} x^{2} - x^{2} \cdot - 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $- 9$ .

$2 x^{2} - 18 - x^{2} x^{2} - x^{2} \cdot - 9$

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

Move $x^{2}$ .

$2 x^{2} - 18 - (x^{2} x^{2}) - x^{2} \cdot - 9$

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

$2 x^{2} - 18 - x^{2 + 2} - x^{2} \cdot - 9$

Add $2$ and $2$ .

$2 x^{2} - 18 - x^{4} - x^{2} \cdot - 9$

Multiply $- 9$ by $- 1$ .

$2 x^{2} - 18 - x^{4} + 9 x^{2}$

Add $2 x^{2}$ and $9 x^{2}$ .

$11 x^{2} - 18 - x^{4}$

Step 3

Move $- 18$ .

$11 x^{2} - x^{4} - 18$

Step 4

Reorder $11 x^{2}$ and $- x^{4}$ .

$- x^{4} + 11 x^{2} - 18$