Algebra Examples

$f (x) = - (x - 3) (x - 5)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$f (x) = (- x + 3) (x - 5)$

Step 2.2

Multiply $- 1$ by $- 3$ .

$f (x) = (- x + 3) (x - 5)$

Step 3

Expand $(- x + 3) (x - 5)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$f (x) = - x (x - 5) + 3 (x - 5)$

Step 3.2

Apply the distributive property.

$f (x) = - x \cdot x - x \cdot - 5 + 3 (x - 5)$

Step 3.3

Apply the distributive property.

$f (x) = - x \cdot x - x \cdot - 5 + 3 x + 3 \cdot - 5$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

Move $x$ .

$f (x) = - (x \cdot x) - x \cdot - 5 + 3 x + 3 \cdot - 5$

Step 4.1.1.2

Multiply $x$ by $x$ .

$f (x) = - x^{2} - x \cdot - 5 + 3 x + 3 \cdot - 5$

Step 4.1.2

Multiply $- 5$ by $- 1$ .

$f (x) = - x^{2} + 5 x + 3 x + 3 \cdot - 5$

Step 4.1.3

Multiply $3$ by $- 5$ .

$f (x) = - x^{2} + 5 x + 3 x - 15$

Step 4.2

Add $5 x$ and $3 x$ .

$f (x) = - x^{2} + 8 x - 15$