Precalculus Examples

j (x) = - x^{2} + 3 x + 10

$j (x) = - x^{2} + 3 x + 10$ ,

j (3 x - 2)

$j (3 x - 2)$

Step 1

Replace the variable

x

$x$ with

3 x - 2

$3 x - 2$ in the expression.

j (3 x - 2) = - {(3 x - 2)}^{2} + 3 (3 x - 2) + 10

$j (3 x - 2) = - {(3 x - 2)}^{2} + 3 (3 x - 2) + 10$

Step 2

Simplify

- {(3 x - 2)}^{2} + 3 (3 x - 2) + 10

$- {(3 x - 2)}^{2} + 3 (3 x - 2) + 10$ .

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Step 2.1

Remove parentheses.

- {(3 x - 2)}^{2} + 3 (3 x - 2) + 10

$- {(3 x - 2)}^{2} + 3 (3 x - 2) + 10$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite

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

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

(3 x - 2) (3 x - 2)

$(3 x - 2) (3 x - 2)$ .

- ((3 x - 2) (3 x - 2)) + 3 (3 x - 2) + 10

$- ((3 x - 2) (3 x - 2)) + 3 (3 x - 2) + 10$

Step 2.2.2

Expand

(3 x - 2) (3 x - 2)

$(3 x - 2) (3 x - 2)$ using the FOIL Method.

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Step 2.2.2.1

Apply the distributive property.

- (3 x (3 x - 2) - 2 (3 x - 2)) + 3 (3 x - 2) + 10

$- (3 x (3 x - 2) - 2 (3 x - 2)) + 3 (3 x - 2) + 10$

Step 2.2.2.2

Apply the distributive property.

- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x - 2)) + 3 (3 x - 2) + 10

$- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x - 2)) + 3 (3 x - 2) + 10$

Step 2.2.2.3

Apply the distributive property.

- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3

Simplify and combine like terms.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Rewrite using the commutative property of multiplication.

- (3 \cdot 3 x \cdot x + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 \cdot 3 x \cdot x + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.2.3.1.2.1

Move

x

$x$ .

- (3 \cdot 3 (x \cdot x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 \cdot 3 (x \cdot x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.2.2

Multiply

x

$x$ by

x

$x$ .

- (3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

- (3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.3

Multiply

3

$3$ by

3

$3$ .

- (9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.4

Multiply

- 2

$- 2$ by

3

$3$ .

- (9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.5

Multiply

3

$3$ by

- 2

$- 2$ .

- (9 x^{2} - 6 x - 6 x - 2 \cdot - 2) + 3 (3 x - 2) + 10

$- (9 x^{2} - 6 x - 6 x - 2 \cdot - 2) + 3 (3 x - 2) + 10$

Step 2.2.3.1.6

Multiply

- 2

$- 2$ by

- 2

$- 2$ .

- (9 x^{2} - 6 x - 6 x + 4) + 3 (3 x - 2) + 10

$- (9 x^{2} - 6 x - 6 x + 4) + 3 (3 x - 2) + 10$

- (9 x^{2} - 6 x - 6 x + 4) + 3 (3 x - 2) + 10

$- (9 x^{2} - 6 x - 6 x + 4) + 3 (3 x - 2) + 10$

Step 2.2.3.2

Subtract

6 x

$6 x$ from

- 6 x

$- 6 x$ .

- (9 x^{2} - 12 x + 4) + 3 (3 x - 2) + 10

$- (9 x^{2} - 12 x + 4) + 3 (3 x - 2) + 10$

- (9 x^{2} - 12 x + 4) + 3 (3 x - 2) + 10

$- (9 x^{2} - 12 x + 4) + 3 (3 x - 2) + 10$

Step 2.2.4

Apply the distributive property.

$- (9 x^{2}) - (- 12 x) - 1 \cdot 4 + 3 (3 x - 2) + 10$

Step 2.2.5

Simplify.

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Step 2.2.5.1

Multiply

$9$ by

$- 1$ .

$- 9 x^{2} - (- 12 x) - 1 \cdot 4 + 3 (3 x - 2) + 10$

Step 2.2.5.2

Multiply

$- 12$ by

$- 1$ .

$- 9 x^{2} + 12 x - 1 \cdot 4 + 3 (3 x - 2) + 10$

Step 2.2.5.3

Multiply

$- 1$ by

$4$ .

$- 9 x^{2} + 12 x - 4 + 3 (3 x - 2) + 10$

Step 2.2.6

Apply the distributive property.

$- 9 x^{2} + 12 x - 4 + 3 (3 x) + 3 \cdot - 2 + 10$

Step 2.2.7

Multiply

$3$ by

$3$ .

$- 9 x^{2} + 12 x - 4 + 9 x + 3 \cdot - 2 + 10$

Step 2.2.8

Multiply

$3$ by

$- 2$ .

$- 9 x^{2} + 12 x - 4 + 9 x - 6 + 10$

Step 2.3

Simplify by adding terms.

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Step 2.3.1

Add

$12 x$ and

$9 x$ .

$- 9 x^{2} + 21 x - 4 - 6 + 10$

Step 2.3.2

Subtract

$6$ from

$- 4$ .

$- 9 x^{2} + 21 x - 10 + 10$

Step 2.3.3

Combine the opposite terms in

$- 9 x^{2} + 21 x - 10 + 10$ .

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Step 2.3.3.1

Add

$- 10$ and

$10$ .

$- 9 x^{2} + 21 x + 0$

Step 2.3.3.2

Add

$- 9 x^{2} + 21 x$ and

$0$ .

$- 9 x^{2} + 21 x$