Evaluate (x^2-9)^2-9

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

Step 1

Simplify each term.

Rewrite ${(x^{2} - 9)}^{2}$ as $(x^{2} - 9) (x^{2} - 9)$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Move $- 9$ to the left of $x^{2}$ .

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

Multiply $- 9$ by $- 9$ .

$x^{4} - 9 x^{2} - 9 x^{2} + 81 - 9$

Subtract $9 x^{2}$ from $- 9 x^{2}$ .

$x^{4} - 18 x^{2} + 81 - 9$

Step 2

Subtract $9$ from $81$ .

$x^{4} - 18 x^{2} + 72$