Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Step 2

Combine the opposite terms in $a \cdot a + a \cdot - 2 + 2 a + 2 \cdot - 2$ .

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Step 2.1

Reorder the factors in the terms $a \cdot - 2$ and $2 a$ .

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

Step 2.2

Add $- 2 a$ and $2 a$ .

$a \cdot a + 0 + 2 \cdot - 2 - a (a - 5)$

Step 2.3

Add $a \cdot a$ and $0$ .

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply $a$ by $a$ .

$a^{2} + 2 \cdot - 2 - a (a - 5)$

Step 3.2

Multiply $2$ by $- 2$ .

$a^{2} - 4 - a (a - 5)$

$a^{2} - 4 - a (a - 5)$

Step 4

Apply the distributive property.

$a^{2} - 4 - a \cdot a - a \cdot - 5$

Step 5

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

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Step 5.1

Move $a$ .

$a^{2} - 4 - (a \cdot a) - a \cdot - 5$

Step 5.2

Multiply $a$ by $a$ .

$a^{2} - 4 - a^{2} - a \cdot - 5$

$a^{2} - 4 - a^{2} - a \cdot - 5$

Step 6

Multiply $- 5$ by $- 1$ .

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

Step 7

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

$0 - 4 + 5 a$

Step 8

Subtract $4$ from $0$ .

$- 4 + 5 a$

Step 9

Factor $- 1$ out of $- 4 + 5 a$ .

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Step 9.1

Reorder $- 4$ and $5 a$ .

$5 a - 4$

Step 9.2

Factor $- 1$ out of $5 a$ .

$- (- 5 a) - 4$

Step 9.3

Rewrite $- 4$ as $- 1 (4)$ .

$- (- 5 a) - 1 (4)$

Step 9.4

Factor $- 1$ out of $- (- 5 a) - 1 (4)$ .

$- (- 5 a + 4)$

$- (- 5 a + 4)$

Step 10

Factor.

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Step 10.1

Factor $- 1$ out of $- 5 a + 4$ .

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Step 10.1.1

Factor $- 1$ out of $- 5 a$ .

$- (- (5 a) + 4)$

Step 10.1.2

Rewrite $4$ as $- 1 (- 4)$ .

$- (- (5 a) - 1 (- 4))$

Step 10.1.3

Factor $- 1$ out of $- (5 a) - 1 (- 4)$ .

$- - (5 a - 4)$

$- - (5 a - 4)$

Step 10.2

Remove unnecessary parentheses.

$- - 1 (5 a - 4)$

$- - 1 (5 a - 4)$

Step 11

Combine exponents.

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Step 11.1

Factor out negative.

$- - (5 a - 4)$

Step 11.2

Multiply $- 1$ by $- 1$ .

$1 (5 a - 4)$

Step 11.3

Multiply $5 a - 4$ by $1$ .

$5 a - 4$

$5 a - 4$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$