Precalculus Examples

$y = 3 (x - 1) (x + 6)$

Step 1

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

$y = a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$y = (3 x + 3 \cdot - 1) (x + 6)$

Step 2.2

Multiply $3$ by $- 1$ .

$y = (3 x - 3) (x + 6)$

Step 3

Expand $(3 x - 3) (x + 6)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$y = 3 x (x + 6) - 3 (x + 6)$

Step 3.2

Apply the distributive property.

$y = 3 x \cdot x + 3 x \cdot 6 - 3 (x + 6)$

Step 3.3

Apply the distributive property.

$y = 3 x \cdot x + 3 x \cdot 6 - 3 x - 3 \cdot 6$

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 $x$ .

$y = 3 (x \cdot x) + 3 x \cdot 6 - 3 x - 3 \cdot 6$

Step 4.1.1.2

Multiply $x$ by $x$ .

$y = 3 x^{2} + 3 x \cdot 6 - 3 x - 3 \cdot 6$

Step 4.1.2

Multiply $6$ by $3$ .

$y = 3 x^{2} + 18 x - 3 x - 3 \cdot 6$

Step 4.1.3

Multiply $- 3$ by $6$ .

$y = 3 x^{2} + 18 x - 3 x - 18$

Step 4.2

Subtract $3 x$ from $18 x$ .

$y = 3 x^{2} + 15 x - 18$

Step 5