Basic Math Examples

$(a + 1) (a + 2) + (- a - 1) (a + 3)$

Step 1

Expand $(a + 1) (a + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$a (a + 2) + 1 (a + 2) + (- a - 1) (a + 3)$

Step 1.2

Apply the distributive property.

$a \cdot a + a \cdot 2 + 1 (a + 2) + (- a - 1) (a + 3)$

Step 1.3

Apply the distributive property.

$a \cdot a + a \cdot 2 + 1 a + 1 \cdot 2 + (- a - 1) (a + 3)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $a$ by $a$ .

$a^{2} + a \cdot 2 + 1 a + 1 \cdot 2 + (- a - 1) (a + 3)$

Step 2.1.2

Move $2$ to the left of $a$ .

$a^{2} + 2 a + 1 a + 1 \cdot 2 + (- a - 1) (a + 3)$

Step 2.1.3

Multiply $a$ by $1$ .

$a^{2} + 2 a + a + 1 \cdot 2 + (- a - 1) (a + 3)$

Step 2.1.4

Multiply $2$ by $1$ .

$a^{2} + 2 a + a + 2 + (- a - 1) (a + 3)$

Step 2.2

Add $2 a$ and $a$ .

$a^{2} + 3 a + 2 + (- a - 1) (a + 3)$

Step 3

Expand $(- a - 1) (a + 3)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$a^{2} + 3 a + 2 - a (a + 3) - 1 (a + 3)$

Step 3.2

Apply the distributive property.

$a^{2} + 3 a + 2 - a \cdot a - a \cdot 3 - 1 (a + 3)$

Step 3.3

Apply the distributive property.

$a^{2} + 3 a + 2 - a \cdot a - a \cdot 3 - 1 a - 1 \cdot 3$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

Move $a$ .

$a^{2} + 3 a + 2 - (a \cdot a) - a \cdot 3 - 1 a - 1 \cdot 3$

Step 4.1.1.2

Multiply $a$ by $a$ .

$a^{2} + 3 a + 2 - a^{2} - a \cdot 3 - 1 a - 1 \cdot 3$

Step 4.1.2

Multiply $3$ by $- 1$ .

$a^{2} + 3 a + 2 - a^{2} - 3 a - 1 a - 1 \cdot 3$

Step 4.1.3

Rewrite $- 1 a$ as $- a$ .

$a^{2} + 3 a + 2 - a^{2} - 3 a - a - 1 \cdot 3$

Step 4.1.4

Multiply $- 1$ by $3$ .

$a^{2} + 3 a + 2 - a^{2} - 3 a - a - 3$

Step 4.2

Subtract $a$ from $- 3 a$ .

$a^{2} + 3 a + 2 - a^{2} - 4 a - 3$

Step 5

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

$3 a + 2 + 0 - 4 a - 3$

Step 6

Add $3 a$ and $0$ .

$3 a + 2 - 4 a - 3$

Step 7

Subtract $4 a$ from $3 a$ .

$- a + 2 - 3$

Step 8

Subtract $3$ from $2$ .

$- a - 1$

Step 9

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

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Step 9.1

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

$- (a) - 1$

Step 9.2

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

$- (a) - 1 (1)$

Step 9.3

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

$- (a + 1)$