Find the Product (p-10q)(p+10q)

$(p - 10 q) (p + 10 q)$

Step 1

Expand $(p - 10 q) (p + 10 q)$ using the FOIL Method.

Apply the distributive property.

$p (p + 10 q) - 10 q (p + 10 q)$

Apply the distributive property.

$p \cdot p + p (10 q) - 10 q (p + 10 q)$

Apply the distributive property.

$p \cdot p + p (10 q) - 10 q p - 10 q (10 q)$

Step 2

Simplify terms.

Combine the opposite terms in $p \cdot p + p (10 q) - 10 q p - 10 q (10 q)$ .

Reorder the factors in the terms $p (10 q)$ and $- 10 q p$ .

$p \cdot p + 10 p q - 10 p q - 10 q (10 q)$

Subtract $10 p q$ from $10 p q$ .

$p \cdot p + 0 - 10 q (10 q)$

Add $p \cdot p$ and $0$ .

$p \cdot p - 10 q (10 q)$

Simplify each term.

Multiply $p$ by $p$ .

$p^{2} - 10 q (10 q)$

Rewrite using the commutative property of multiplication.

$p^{2} - 10 \cdot 10 q \cdot q$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$p^{2} - 10 \cdot 10 (q \cdot q)$

Multiply $q$ by $q$ .

$p^{2} - 10 \cdot 10 q^{2}$

Multiply $- 10$ by $10$ .

$p^{2} - 100 q^{2}$