Algebra Examples

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

Step 1

Expand $(m + p) (m^{2} - 2 m p + p^{2})$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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Step 2.1.1.1

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

$m^{1} m^{2} + m (- 2 m p) + m p^{2} + p m^{2} + p (- 2 m p) + p \cdot p^{2}$

Step 2.1.1.2

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

$m^{1 + 2} + m (- 2 m p) + m p^{2} + p m^{2} + p (- 2 m p) + p \cdot p^{2}$

Step 2.1.2

Add $1$ and $2$ .

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Multiply $m$ by $m$ by adding the exponents.

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Step 2.3.1

Move $m$ .

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

Step 2.3.2

Multiply $m$ by $m$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

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

Step 2.5

Multiply $p$ by $p$ by adding the exponents.

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Step 2.5.1

Move $p$ .

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

Step 2.5.2

Multiply $p$ by $p$ .

$m^{3} - 2 m^{2} p + m p^{2} + p m^{2} - 2 p^{2} m + p \cdot p^{2}$

Step 2.6

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

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Step 2.6.1

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

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Step 2.6.1.1

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

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

Step 2.6.1.2

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

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

Step 2.6.2

Add $1$ and $2$ .

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

Step 3

Add $- 2 m^{2} p$ and $p m^{2}$ .

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Step 3.1

Reorder $p$ and $m^{2}$ .

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

Step 3.2

Add $- 2 m^{2} p$ and $m^{2} p$ .

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

Step 4

Subtract $2 p^{2} m$ from $m p^{2}$ .

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Step 4.1

Move $p^{2}$ .

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

Step 4.2

Subtract $2 m p^{2}$ from $m p^{2}$ .

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