Basic Math Examples

$5 (a - 2) - (a + 2) (a - 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 a + 5 \cdot - 2 - (a + 2) (a - 2)$

Step 1.2

Multiply $5$ by $- 2$ .

$5 a - 10 - (a + 2) (a - 2)$

Step 1.3

Apply the distributive property.

$5 a - 10 + (- a - 1 \cdot 2) (a - 2)$

Step 1.4

Multiply $- 1$ by $2$ .

$5 a - 10 + (- a - 2) (a - 2)$

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

$5 a - 10 - a (a - 2) - 2 (a - 2)$

Step 1.5.2

Apply the distributive property.

$5 a - 10 - a \cdot a - a \cdot - 2 - 2 (a - 2)$

Step 1.5.3

Apply the distributive property.

$5 a - 10 - a \cdot a - a \cdot - 2 - 2 a - 2 \cdot - 2$

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $a$ by $a$ by adding the exponents.

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Step 1.6.1.1.1

Move $a$ .

$5 a - 10 - (a \cdot a) - a \cdot - 2 - 2 a - 2 \cdot - 2$

Step 1.6.1.1.2

Multiply $a$ by $a$ .

$5 a - 10 - a^{2} - a \cdot - 2 - 2 a - 2 \cdot - 2$

Step 1.6.1.2

Multiply $- 2$ by $- 1$ .

$5 a - 10 - a^{2} + 2 a - 2 a - 2 \cdot - 2$

Step 1.6.1.3

Multiply $- 2$ by $- 2$ .

$5 a - 10 - a^{2} + 2 a - 2 a + 4$

Step 1.6.2

Subtract $2 a$ from $2 a$ .

$5 a - 10 - a^{2} + 0 + 4$

Step 1.6.3

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

$5 a - 10 - a^{2} + 4$

Step 2

Simplify the expression.

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Step 2.1

Add $- 10$ and $4$ .

$5 a - a^{2} - 6$

Step 2.2

Reorder $5 a$ and $- a^{2}$ .

$- a^{2} + 5 a - 6$