Finite Math Examples

$(x^{2} - 2) (17 - x)$

Step 1

Expand $(x^{2} - 2) (17 - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x^{2} (17 - x) - 2 (17 - x)$

Step 1.2

Apply the distributive property.

$x^{2} \cdot 17 + x^{2} (- x) - 2 (17 - x)$

Step 1.3

Apply the distributive property.

$x^{2} \cdot 17 + x^{2} (- x) - 2 \cdot 17 - 2 (- x)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $17$ to the left of $x^{2}$ .

$17 \cdot x^{2} + x^{2} (- x) - 2 \cdot 17 - 2 (- x)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$17 x^{2} - x^{2} x - 2 \cdot 17 - 2 (- x)$

Step 2.1.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.1.3.1

Move $x$ .

$17 x^{2} - (x \cdot x^{2}) - 2 \cdot 17 - 2 (- x)$

Step 2.1.3.2

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

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Step 2.1.3.2.1

Raise $x$ to the power of $1$ .

$17 x^{2} - (x^{1} x^{2}) - 2 \cdot 17 - 2 (- x)$

Step 2.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$17 x^{2} - x^{1 + 2} - 2 \cdot 17 - 2 (- x)$

Step 2.1.3.3

Add $1$ and $2$ .

$17 x^{2} - x^{3} - 2 \cdot 17 - 2 (- x)$

Step 2.1.4

Multiply $- 2$ by $17$ .

$17 x^{2} - x^{3} - 34 - 2 (- x)$

Step 2.1.5

Multiply $- 1$ by $- 2$ .

$17 x^{2} - x^{3} - 34 + 2 x$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 34$ .

$17 x^{2} - x^{3} + 2 x - 34$

Step 2.2.2

Reorder $17 x^{2}$ and $- x^{3}$ .

$- x^{3} + 17 x^{2} + 2 x - 34$