Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(m - 2)}^{2}$ as $(m - 2) (m - 2)$ .

$(m - 2) (m - 2) - (m - 2) (m + 2)$

Step 1.2

Expand $(m - 2) (m - 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$m (m - 2) - 2 (m - 2) - (m - 2) (m + 2)$

Step 1.2.2

Apply the distributive property.

$m \cdot m + m \cdot - 2 - 2 (m - 2) - (m - 2) (m + 2)$

Step 1.2.3

Apply the distributive property.

$m \cdot m + m \cdot - 2 - 2 m - 2 \cdot - 2 - (m - 2) (m + 2)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $m$ by $m$ .

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

Step 1.3.1.2

Move $- 2$ to the left of $m$ .

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

Step 1.3.1.3

Multiply $- 2$ by $- 2$ .

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

Step 1.3.2

Subtract $2 m$ from $- 2 m$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- 1$ by $- 2$ .

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

Step 1.6

Expand $(- m + 2) (m + 2)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

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

Step 1.6.2

Apply the distributive property.

$m^{2} - 4 m + 4 - m \cdot m - m \cdot 2 + 2 (m + 2)$

Step 1.6.3

Apply the distributive property.

$m^{2} - 4 m + 4 - m \cdot m - m \cdot 2 + 2 m + 2 \cdot 2$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

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

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Step 1.7.1.1.1

Move $m$ .

$m^{2} - 4 m + 4 - (m \cdot m) - m \cdot 2 + 2 m + 2 \cdot 2$

Step 1.7.1.1.2

Multiply $m$ by $m$ .

$m^{2} - 4 m + 4 - m^{2} - m \cdot 2 + 2 m + 2 \cdot 2$

Step 1.7.1.2

Multiply $2$ by $- 1$ .

$m^{2} - 4 m + 4 - m^{2} - 2 m + 2 m + 2 \cdot 2$

Step 1.7.1.3

Multiply $2$ by $2$ .

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

Step 1.7.2

Add $- 2 m$ and $2 m$ .

$m^{2} - 4 m + 4 - m^{2} + 0 + 4$

Step 1.7.3

Add $- m^{2}$ and $0$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $m^{2} - 4 m + 4 - m^{2} + 4$ .

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Step 2.1.1

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

$- 4 m + 4 + 0 + 4$

Step 2.1.2

Add $- 4 m + 4$ and $0$ .

$- 4 m + 4 + 4$

Step 2.2

Add $4$ and $4$ .

$- 4 m + 8$