Precalculus Examples

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

Step 1

Replace the variable $x$ with $3 x - 2$ in the expression.

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

Step 2

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

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Step 2.1

Remove parentheses.

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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

Step 2.2.2

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

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Step 2.2.2.1

Apply the distributive property.

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

Step 2.2.2.2

Apply the distributive property.

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

Step 2.2.2.3

Apply the distributive property.

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

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.

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

Step 2.2.3.1.2

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

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Step 2.2.3.1.2.1

Move $x$ .

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

Step 2.2.3.1.2.2

Multiply $x$ by $x$ .

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

Step 2.2.3.1.3

Multiply $3$ by $3$ .

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

Step 2.2.3.1.4

Multiply $- 2$ by $3$ .

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

Step 2.2.3.1.5

Multiply $3$ by $- 2$ .

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

Step 2.2.3.1.6

Multiply $- 2$ by $- 2$ .

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

Step 2.2.3.2

Subtract $6 x$ from $- 6 x$ .

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

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 $0$ .

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