Precalculus Examples

$f (x) = x (x - 8)$ , $f (x - 3)$

Step 1

Replace the variable $x$ with $x - 3$ in the expression.

$f (x - 3) = (x - 3) ((x - 3) - 8)$

Step 2

Simplify $(x - 3) ((x - 3) - 8)$ .

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Step 2.1

Simplify the expression.

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Step 2.1.1

Remove parentheses.

$(x - 3) ((x - 3) - 8)$

Step 2.1.2

Subtract $8$ from $- 3$ .

$(x - 3) (x - 11)$

$(x - 3) (x - 11)$

Step 2.2

Expand $(x - 3) (x - 11)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$x (x - 11) - 3 (x - 11)$

Step 2.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 3 (x - 11)$

Step 2.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 3 x - 3 \cdot - 11$

$x \cdot x + x \cdot - 11 - 3 x - 3 \cdot - 11$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 11 - 3 x - 3 \cdot - 11$

Step 2.3.1.2

Move $- 11$ to the left of $x$ .

$x^{2} - 11 \cdot x - 3 x - 3 \cdot - 11$

Step 2.3.1.3

Multiply $- 3$ by $- 11$ .

$x^{2} - 11 x - 3 x + 33$

$x^{2} - 11 x - 3 x + 33$

Step 2.3.2

Subtract $3 x$ from $- 11 x$ .

$x^{2} - 14 x + 33$

$x^{2} - 14 x + 33$

$x^{2} - 14 x + 33$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$