Basic Math Examples

$(m - 5) (m^{2} - 2 m p + 3 p^{2})$

Step 1

Expand $(m - 5) (m^{2} - 2 m p + 3 p^{2})$ by multiplying each term in the first expression by each term in the second expression.

$m \cdot m^{2} + m (- 2 m p) + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$m^{1} m^{2} + m (- 2 m p) + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.1.1.2

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

$m^{1 + 2} + m (- 2 m p) + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.1.2

Add $1$ and $2$ .

$m^{3} + m (- 2 m p) + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$m^{3} - 2 m (m p) + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.3

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

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Step 2.1.3.1

Move $m$ .

$m^{3} - 2 (m \cdot m) p + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.3.2

Multiply $m$ by $m$ .

$m^{3} - 2 m^{2} p + m (3 p^{2}) - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$m^{3} - 2 m^{2} p + 3 m p^{2} - 5 m^{2} - 5 (- 2 m p) - 5 (3 p^{2})$

Step 2.1.5

Multiply $- 2$ by $- 5$ .

$m^{3} - 2 m^{2} p + 3 m p^{2} - 5 m^{2} + 10 (m p) - 5 (3 p^{2})$

Step 2.1.6

Multiply $3$ by $- 5$ .

$m^{3} - 2 m^{2} p + 3 m p^{2} - 5 m^{2} + 10 m p - 15 p^{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 5 m^{2}$ .

$m^{3} - 2 m^{2} p + 3 m p^{2} + 10 m p - 15 p^{2} - 5 m^{2}$

Step 2.2.2

Move $10 m p$ .

$m^{3} - 2 m^{2} p + 3 m p^{2} - 15 p^{2} + 10 m p - 5 m^{2}$

Step 2.2.3

Move $m^{3}$ .

$- 2 m^{2} p + 3 m p^{2} + m^{3} - 15 p^{2} + 10 m p - 5 m^{2}$

Step 2.2.4

Reorder $- 2 m^{2} p$ and $3 m p^{2}$ .

$3 m p^{2} - 2 m^{2} p + m^{3} - 15 p^{2} + 10 m p - 5 m^{2}$