Algebra Examples

$f (x) = 5 x - 1$ , $g (x) = 2 x + 1$

Step 1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(5 x - 1) \cdot (2 x + 1)$

Step 2

Simplify.

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Step 2.1

Expand $(5 x - 1) (2 x + 1)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$5 x (2 x + 1) - 1 (2 x + 1)$

Step 2.1.2

Apply the distributive property.

$5 x (2 x) + 5 x \cdot 1 - 1 (2 x + 1)$

Step 2.1.3

Apply the distributive property.

$5 x (2 x) + 5 x \cdot 1 - 1 (2 x) - 1 \cdot 1$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x \cdot x + 5 x \cdot 1 - 1 (2 x) - 1 \cdot 1$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$5 \cdot 2 (x \cdot x) + 5 x \cdot 1 - 1 (2 x) - 1 \cdot 1$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$5 \cdot 2 x^{2} + 5 x \cdot 1 - 1 (2 x) - 1 \cdot 1$

Step 2.2.1.3

Multiply $5$ by $2$ .

$10 x^{2} + 5 x \cdot 1 - 1 (2 x) - 1 \cdot 1$

Step 2.2.1.4

Multiply $5$ by $1$ .

$10 x^{2} + 5 x - 1 (2 x) - 1 \cdot 1$

Step 2.2.1.5

Multiply $2$ by $- 1$ .

$10 x^{2} + 5 x - 2 x - 1 \cdot 1$

Step 2.2.1.6

Multiply $- 1$ by $1$ .

$10 x^{2} + 5 x - 2 x - 1$

Step 2.2.2

Subtract $2 x$ from $5 x$ .

$10 x^{2} + 3 x - 1$

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