Precalculus Examples

$y = - 3 (x - 1) (x + 7)$

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.

$y = (- 3 x - 3 \cdot - 1) (x + 7)$

Step 2.2

Multiply $- 3$ by $- 1$ .

$y = (- 3 x + 3) (x + 7)$

Step 3

Expand $(- 3 x + 3) (x + 7)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$y = - 3 x (x + 7) + 3 (x + 7)$

Step 3.2

Apply the distributive property.

$y = - 3 x \cdot x - 3 x \cdot 7 + 3 (x + 7)$

Step 3.3

Apply the distributive property.

$y = - 3 x \cdot x - 3 x \cdot 7 + 3 x + 3 \cdot 7$

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 $x$ .

$y = - 3 (x \cdot x) - 3 x \cdot 7 + 3 x + 3 \cdot 7$

Step 4.1.1.2

Multiply $x$ by $x$ .

$y = - 3 x^{2} - 3 x \cdot 7 + 3 x + 3 \cdot 7$

Step 4.1.2

Multiply $7$ by $- 3$ .

$y = - 3 x^{2} - 21 x + 3 x + 3 \cdot 7$

Step 4.1.3

Multiply $3$ by $7$ .

$y = - 3 x^{2} - 21 x + 3 x + 21$

Step 4.2

Add $- 21 x$ and $3 x$ .

$y = - 3 x^{2} - 18 x + 21$

Step 5