Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $p$ by $p$ .

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

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

Step 2.2.3

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

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Step 2.2.3.1

Move $r$ .

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

Step 2.2.3.2

Multiply $r$ by $r$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

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

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

Step 4.1.1.2

Add $2$ and $1$ .

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

Step 4.1.2

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

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Step 4.1.2.1

Move $r$ .

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

Step 4.1.2.2

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

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Step 4.1.2.2.1

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

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

Step 4.1.2.2.2

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

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

Step 4.1.2.3

Add $1$ and $2$ .

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

Step 4.2

Move $r^{2}$ .

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