Basic Math Examples

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

Step 1

Expand $(m n^{2} - p) (m n^{2} - p)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $m$ .

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

Step 2.1.1.2

Multiply $m$ by $m$ .

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

Step 2.1.2

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

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Step 2.1.2.1

Move $n^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $2$ .

$m^{2} n^{4} + m n^{2} (- p) - p (m n^{2}) - p (- p)$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$m^{2} n^{4} - m n^{2} p - p (m n^{2}) - p (- p)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$m^{2} n^{4} - m n^{2} p - p m n^{2} - 1 \cdot - 1 p \cdot p$

Step 2.1.5

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

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Step 2.1.5.1

Move $p$ .

$m^{2} n^{4} - m n^{2} p - p m n^{2} - 1 \cdot - 1 (p \cdot p)$

Step 2.1.5.2

Multiply $p$ by $p$ .

$m^{2} n^{4} - m n^{2} p - p m n^{2} - 1 \cdot - 1 p^{2}$

Step 2.1.6

Multiply $- 1$ by $- 1$ .

$m^{2} n^{4} - m n^{2} p - p m n^{2} + 1 p^{2}$

Step 2.1.7

Multiply $p^{2}$ by $1$ .

$m^{2} n^{4} - m n^{2} p - p m n^{2} + p^{2}$

Step 2.2

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

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Step 2.2.1

Move $p$ .

$m^{2} n^{4} - m n^{2} p - 1 m n^{2} p + p^{2}$

Step 2.2.2

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

$m^{2} n^{4} - 2 m n^{2} p + p^{2}$