Algebra Examples

$f (x) = (3 x - 4) (- 6 x + 5)$

Step 1

Simplify $f (x)$ .

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Step 1.1

Expand $(3 x - 4) (- 6 x + 5)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$f (x) = 3 x (- 6 x + 5) - 4 (- 6 x + 5)$

Step 1.1.2

Apply the distributive property.

$f (x) = 3 x (- 6 x) + 3 x \cdot 5 - 4 (- 6 x + 5)$

Step 1.1.3

Apply the distributive property.

$f (x) = 3 x (- 6 x) + 3 x \cdot 5 - 4 (- 6 x) - 4 \cdot 5$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$f (x) = 3 \cdot (- 6 x \cdot x) + 3 x \cdot 5 - 4 (- 6 x) - 4 \cdot 5$

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

$f (x) = 3 \cdot (- 6 (x \cdot x)) + 3 x \cdot 5 - 4 (- 6 x) - 4 \cdot 5$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$f (x) = 3 \cdot (- 6 x^{2}) + 3 x \cdot 5 - 4 (- 6 x) - 4 \cdot 5$

Step 1.2.1.3

Multiply $3$ by $- 6$ .

$f (x) = - 18 x^{2} + 3 x \cdot 5 - 4 (- 6 x) - 4 \cdot 5$

Step 1.2.1.4

Multiply $5$ by $3$ .

$f (x) = - 18 x^{2} + 15 x - 4 (- 6 x) - 4 \cdot 5$

Step 1.2.1.5

Multiply $- 6$ by $- 4$ .

$f (x) = - 18 x^{2} + 15 x + 24 x - 4 \cdot 5$

Step 1.2.1.6

Multiply $- 4$ by $5$ .

$f (x) = - 18 x^{2} + 15 x + 24 x - 20$

Step 1.2.2

Add $15 x$ and $24 x$ .

$f (x) = - 18 x^{2} + 39 x - 20$

Step 2

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be $0$ or $1$ . In this case, The degree of $f (x) = - 18 x^{2} + 39 x - 20$ is $2$ , which makes the function a nonlinear function.

$f (x) = - 18 x^{2} + 39 x - 20$ is not a linear function