Basic Math Examples

$(4 + a) (4 - a) - 12 - 3 a$

Step 1

Factor $- 1$ out of $(4 + a) (4 - a) - 12 - 3 a$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $4$ and $a$ .

$(a + 4) (4 - a) - 12 - 3 a$

Step 1.1.2

Reorder $4$ and $- a$ .

$(a + 4) (- a + 4) - 12 - 3 a$

Step 1.1.3

Move $- 12$ .

$(a + 4) (- a + 4) - 3 a - 12$

Step 1.2

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

$- ((- a - 4) (- a + 4)) - 3 a - 12$

Step 1.3

Factor $- 1$ out of $- 3 a$ .

$- ((- a - 4) (- a + 4)) - (3 a) - 12$

Step 1.4

Rewrite $- 12$ as $- 1 (12)$ .

$- ((- a - 4) (- a + 4)) - (3 a) - 1 (12)$

Step 1.5

Factor $- 1$ out of $- ((- a - 4) (- a + 4)) - (3 a)$ .

$- ((- a - 4) (- a + 4) + 3 a) - 1 (12)$

Step 1.6

Factor $- 1$ out of $- ((- a - 4) (- a + 4) + 3 a) - 1 (12)$ .

$- ((- a - 4) (- a + 4) + 3 a + 12)$

Step 2

Expand $(- a - 4) (- a + 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- (- a (- a + 4) - 4 (- a + 4) + 3 a + 12)$

Step 2.2

Apply the distributive property.

$- (- a (- a) - a \cdot 4 - 4 (- a + 4) + 3 a + 12)$

Step 2.3

Apply the distributive property.

$- (- a (- a) - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$- (- 1 \cdot - 1 a \cdot a - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.2

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

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Step 3.1.2.1

Move $a$ .

$- (- 1 \cdot - 1 (a \cdot a) - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.2.2

Multiply $a$ by $a$ .

$- (- 1 \cdot - 1 a^{2} - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.3

Multiply $- 1$ by $- 1$ .

$- (1 a^{2} - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.4

Multiply $a^{2}$ by $1$ .

$- (a^{2} - a \cdot 4 - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.5

Multiply $4$ by $- 1$ .

$- (a^{2} - 4 a - 4 (- a) - 4 \cdot 4 + 3 a + 12)$

Step 3.1.6

Multiply $- 1$ by $- 4$ .

$- (a^{2} - 4 a + 4 a - 4 \cdot 4 + 3 a + 12)$

Step 3.1.7

Multiply $- 4$ by $4$ .

$- (a^{2} - 4 a + 4 a - 16 + 3 a + 12)$

Step 3.2

Add $- 4 a$ and $4 a$ .

$- (a^{2} + 0 - 16 + 3 a + 12)$

Step 3.3

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

$- (a^{2} - 16 + 3 a + 12)$

Step 4

Add $- 16$ and $12$ .

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

Step 5

Factor.

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Step 5.1

Factor $a^{2} + 3 a - 4$ using the AC method.

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Step 5.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 4$ and whose sum is $3$ .

$- 1, 4$

Step 5.1.2

Write the factored form using these integers.

$- ((a - 1) (a + 4))$

Step 5.2

Remove unnecessary parentheses.

$- (a - 1) (a + 4)$