Precalculus Examples

$f (x) = 2 x^{2} + 5 x - 9$ , $f (5 x - 2)$

Step 1

Replace the variable $x$ with $5 x - 2$ in the expression.

$f (5 x - 2) = 2 {(5 x - 2)}^{2} + 5 (5 x - 2) - 9$

Step 2

Simplify $2 {(5 x - 2)}^{2} + 5 (5 x - 2) - 9$ .

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Step 2.1

Remove parentheses.

$2 {(5 x - 2)}^{2} + 5 (5 x - 2) - 9$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite ${(5 x - 2)}^{2}$ as $(5 x - 2) (5 x - 2)$ .

$2 ((5 x - 2) (5 x - 2)) + 5 (5 x - 2) - 9$

Step 2.2.2

Expand $(5 x - 2) (5 x - 2)$ using the FOIL Method.

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Step 2.2.2.1

Apply the distributive property.

$2 (5 x (5 x - 2) - 2 (5 x - 2)) + 5 (5 x - 2) - 9$

Step 2.2.2.2

Apply the distributive property.

$2 (5 x (5 x) + 5 x \cdot - 2 - 2 (5 x - 2)) + 5 (5 x - 2) - 9$

Step 2.2.2.3

Apply the distributive property.

$2 (5 x (5 x) + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

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.

$2 (5 \cdot 5 x \cdot x + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

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 $x$ .

$2 (5 \cdot 5 (x \cdot x) + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

Step 2.2.3.1.2.2

Multiply $x$ by $x$ .

$2 (5 \cdot 5 x^{2} + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

Step 2.2.3.1.3

Multiply $5$ by $5$ .

$2 (25 x^{2} + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

Step 2.2.3.1.4

Multiply $- 2$ by $5$ .

$2 (25 x^{2} - 10 x - 2 (5 x) - 2 \cdot - 2) + 5 (5 x - 2) - 9$

Step 2.2.3.1.5

Multiply $5$ by $- 2$ .

$2 (25 x^{2} - 10 x - 10 x - 2 \cdot - 2) + 5 (5 x - 2) - 9$

Step 2.2.3.1.6

Multiply $- 2$ by $- 2$ .

$2 (25 x^{2} - 10 x - 10 x + 4) + 5 (5 x - 2) - 9$

Step 2.2.3.2

Subtract $10 x$ from $- 10 x$ .

$2 (25 x^{2} - 20 x + 4) + 5 (5 x - 2) - 9$

Step 2.2.4

Apply the distributive property.

$2 (25 x^{2}) + 2 (- 20 x) + 2 \cdot 4 + 5 (5 x - 2) - 9$

Step 2.2.5

Simplify.

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Step 2.2.5.1

Multiply $25$ by $2$ .

$50 x^{2} + 2 (- 20 x) + 2 \cdot 4 + 5 (5 x - 2) - 9$

Step 2.2.5.2

Multiply $- 20$ by $2$ .

$50 x^{2} - 40 x + 2 \cdot 4 + 5 (5 x - 2) - 9$

Step 2.2.5.3

Multiply $2$ by $4$ .

$50 x^{2} - 40 x + 8 + 5 (5 x - 2) - 9$

Step 2.2.6

Apply the distributive property.

$50 x^{2} - 40 x + 8 + 5 (5 x) + 5 \cdot - 2 - 9$

Step 2.2.7

Multiply $5$ by $5$ .

$50 x^{2} - 40 x + 8 + 25 x + 5 \cdot - 2 - 9$

Step 2.2.8

Multiply $5$ by $- 2$ .

$50 x^{2} - 40 x + 8 + 25 x - 10 - 9$

Step 2.3

Simplify by adding terms.

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Step 2.3.1

Add $- 40 x$ and $25 x$ .

$50 x^{2} - 15 x + 8 - 10 - 9$

Step 2.3.2

Simplify by subtracting numbers.

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Step 2.3.2.1

Subtract $10$ from $8$ .

$50 x^{2} - 15 x - 2 - 9$

Step 2.3.2.2

Subtract $9$ from $- 2$ .

$50 x^{2} - 15 x - 11$