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Simplify (9-z)(9+z)

$(9 - z) (9 + z)$

Step 1

Expand $(9 - z) (9 + z)$ using the FOIL Method.

Apply the distributive property.

$9 (9 + z) - z (9 + z)$

Apply the distributive property.

$9 \cdot 9 + 9 z - z (9 + z)$

Apply the distributive property.

$9 \cdot 9 + 9 z - z \cdot 9 - z \cdot z$

$9 \cdot 9 + 9 z - z \cdot 9 - z \cdot z$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 z - z \cdot 9 - z \cdot z$

Multiply $9$ by $- 1$ .

$81 + 9 z - 9 z - z \cdot z$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$81 + 9 z - 9 z - (z \cdot z)$

Multiply $z$ by $z$ .

$81 + 9 z - 9 z - z^{2}$

$81 + 9 z - 9 z - z^{2}$

$81 + 9 z - 9 z - z^{2}$

Subtract $9 z$ from $9 z$ .

$81 + 0 - z^{2}$

Add $81$ and $0$ .

$81 - z^{2}$

$81 - z^{2}$

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