Finite Math Examples

$(16 - x) (12 - x)$

Step 1

Expand $(16 - x) (12 - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$16 (12 - x) - x (12 - x)$

Step 1.2

Apply the distributive property.

$16 \cdot 12 + 16 (- x) - x (12 - x)$

Step 1.3

Apply the distributive property.

$16 \cdot 12 + 16 (- x) - x \cdot 12 - x (- x)$

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 $16$ by $12$ .

$192 + 16 (- x) - x \cdot 12 - x (- x)$

Step 2.1.2

Multiply $- 1$ by $16$ .

$192 - 16 x - x \cdot 12 - x (- x)$

Step 2.1.3

Multiply $12$ by $- 1$ .

$192 - 16 x - 12 x - x (- x)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$192 - 16 x - 12 x - 1 \cdot - 1 x \cdot x$

Step 2.1.5

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.5.1

Move $x$ .

$192 - 16 x - 12 x - 1 \cdot - 1 (x \cdot x)$

Step 2.1.5.2

Multiply $x$ by $x$ .

$192 - 16 x - 12 x - 1 \cdot - 1 x^{2}$

Step 2.1.6

Multiply $- 1$ by $- 1$ .

$192 - 16 x - 12 x + 1 x^{2}$

Step 2.1.7

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

$192 - 16 x - 12 x + x^{2}$

Step 2.2

Subtract $12 x$ from $- 16 x$ .

$192 - 28 x + x^{2}$

Step 3

Factor $192 - 28 x + x^{2}$ using the AC method.

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Step 3.1

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 $192$ and whose sum is $- 28$ .

$- 16, - 12$

Step 3.2

Write the factored form using these integers.

$(x - 16) (x - 12)$