Basic Math Examples

$y = (m^{2} - 100) \cdot (- (m^{2} - 10 m))$

Step 1

Remove parentheses.

$y = (m^{2} - 100) \cdot (- 1 (m^{2} - 10 m))$

Step 2

Simplify $(m^{2} - 100) \cdot (- 1 (m^{2} - 10 m))$ .

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

$y = (m^{2} - 100) \cdot (- 1 m^{2} - 1 (- 10 m))$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Rewrite $- 1 m^{2}$ as $- m^{2}$ .

$y = (m^{2} - 100) \cdot (- m^{2} - 1 (- 10 m))$

Step 2.1.2.2

Multiply $- 10$ by $- 1$ .

$y = (m^{2} - 100) \cdot (- m^{2} + 10 m)$

Step 2.2

Expand $(m^{2} - 100) (- m^{2} + 10 m)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$y = m^{2} (- m^{2} + 10 m) - 100 (- m^{2} + 10 m)$

Step 2.2.2

Apply the distributive property.

$y = m^{2} (- m^{2}) + m^{2} (10 m) - 100 (- m^{2} + 10 m)$

Step 2.2.3

Apply the distributive property.

$y = m^{2} (- m^{2}) + m^{2} (10 m) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3

Simplify each term.

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Step 2.3.1

Rewrite using the commutative property of multiplication.

$y = - m^{2} m^{2} + m^{2} (10 m) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.2

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

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Step 2.3.2.1

Move $m^{2}$ .

$y = - (m^{2} m^{2}) + m^{2} (10 m) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.2.2

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

$y = - m^{2 + 2} + m^{2} (10 m) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.2.3

Add $2$ and $2$ .

$y = - m^{4} + m^{2} (10 m) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.3

Rewrite using the commutative property of multiplication.

$y = - m^{4} + 10 m^{2} m - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.4

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

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Step 2.3.4.1

Move $m$ .

$y = - m^{4} + 10 (m \cdot m^{2}) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.4.2

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

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Step 2.3.4.2.1

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

$y = - m^{4} + 10 (m^{1} m^{2}) - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.4.2.2

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

$y = - m^{4} + 10 m^{1 + 2} - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.4.3

Add $1$ and $2$ .

$y = - m^{4} + 10 m^{3} - 100 (- m^{2}) - 100 (10 m)$

Step 2.3.5

Multiply $- 1$ by $- 100$ .

$y = - m^{4} + 10 m^{3} + 100 m^{2} - 100 (10 m)$

Step 2.3.6

Multiply $10$ by $- 100$ .

$y = - m^{4} + 10 m^{3} + 100 m^{2} - 1000 m$