Simplify (p+r)(p-r)(p+r)

$(p + r) (p - r) (p + r)$

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

Apply the distributive property.

$(p (p - r) + r (p - r)) (p + r)$

Apply the distributive property.

$(p \cdot p + p (- r) + r (p - r)) (p + r)$

Apply the distributive property.

$(p \cdot p + p (- r) + r p + r (- r)) (p + r)$

Simplify terms.

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

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

$(p \cdot p - p r + p r + r (- r)) (p + r)$

Add $- p r$ and $p r$ .

$(p \cdot p + 0 + r (- r)) (p + r)$

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

$(p \cdot p + r (- r)) (p + r)$

Simplify each term.

Multiply $p$ by $p$ .

$(p^{2} + r (- r)) (p + r)$

Rewrite using the commutative property of multiplication.

$(p^{2} - r \cdot r) (p + r)$

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$(p^{2} - (r \cdot r)) (p + r)$

Multiply $r$ by $r$ .

$(p^{2} - r^{2}) (p + r)$

Expand $(p^{2} - r^{2}) (p + r)$ using the FOIL Method.

Apply the distributive property.

$p^{2} (p + r) - r^{2} (p + r)$

Apply the distributive property.

$p^{2} p + p^{2} r - r^{2} (p + r)$

Apply the distributive property.

$p^{2} p + p^{2} r - r^{2} p - r^{2} r$

Simplify terms.

Simplify each term.

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

Multiply $p^{2}$ by $p$ .

Raise $p$ to the power of $1$ .

$p^{2} p^{1} + p^{2} r - r^{2} p - r^{2} r$

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

$p^{2 + 1} + p^{2} r - r^{2} p - r^{2} r$

Add $2$ and $1$ .

$p^{3} + p^{2} r - r^{2} p - r^{2} r$

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

Move $r$ .

$p^{3} + p^{2} r - r^{2} p - (r \cdot r^{2})$

Multiply $r$ by $r^{2}$ .

Raise $r$ to the power of $1$ .

$p^{3} + p^{2} r - r^{2} p - (r^{1} r^{2})$

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

$p^{3} + p^{2} r - r^{2} p - r^{1 + 2}$

Add $1$ and $2$ .

$p^{3} + p^{2} r - r^{2} p - r^{3}$

Move $r^{2}$ .

$p^{3} + p^{2} r - 1 p r^{2} - r^{3}$

Simplify (p+r)(p-r)(p+r)

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