Precalculus Examples

$(9 - x^{2}) (3 - x)$

Step 1

Expand $(9 - x^{2}) (3 - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 (3 - x) - x^{2} (3 - x)$

Step 1.2

Apply the distributive property.

$9 \cdot 3 + 9 (- x) - x^{2} (3 - x)$

Step 1.3

Apply the distributive property.

$9 \cdot 3 + 9 (- x) - x^{2} \cdot 3 - x^{2} (- x)$

Step 2

Simplify each term.

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Step 2.1

Multiply $9$ by $3$ .

$27 + 9 (- x) - x^{2} \cdot 3 - x^{2} (- x)$

Step 2.2

Multiply $- 1$ by $9$ .

$27 - 9 x - x^{2} \cdot 3 - x^{2} (- x)$

Step 2.3

Multiply $3$ by $- 1$ .

$27 - 9 x - 3 x^{2} - x^{2} (- x)$

Step 2.4

Rewrite using the commutative property of multiplication.

$27 - 9 x - 3 x^{2} - 1 \cdot - 1 x^{2} x$

Step 2.5

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

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Step 2.5.1

Move $x$ .

$27 - 9 x - 3 x^{2} - 1 \cdot - 1 (x \cdot x^{2})$

Step 2.5.2

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

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Step 2.5.2.1

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

$27 - 9 x - 3 x^{2} - 1 \cdot - 1 (x^{1} x^{2})$

Step 2.5.2.2

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

$27 - 9 x - 3 x^{2} - 1 \cdot - 1 x^{1 + 2}$

Step 2.5.3

Add $1$ and $2$ .

$27 - 9 x - 3 x^{2} - 1 \cdot - 1 x^{3}$

Step 2.6

Multiply $- 1$ by $- 1$ .

$27 - 9 x - 3 x^{2} + 1 x^{3}$

Step 2.7

Multiply $x^{3}$ by $1$ .

$27 - 9 x - 3 x^{2} + x^{3}$