Algebra Examples

f (x) = x^{2} + 2 x + 1

$f (x) = x^{2} + 2 x + 1$ ,

g (x) = x

$g (x) = x$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in

f (x) \cdot (g (x))

$f (x) \cdot (g (x))$ .

(x^{2} + 2 x + 1) \cdot (x)

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

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

x^{2} x + 2 x \cdot x + 1 x

$x^{2} x + 2 x \cdot x + 1 x$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 1.2.2.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ .

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Step 1.2.2.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

x^{2} x^{1} + 2 x \cdot x + 1 x

$x^{2} x^{1} + 2 x \cdot x + 1 x$

Step 1.2.2.1.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

x^{2 + 1} + 2 x \cdot x + 1 x

$x^{2 + 1} + 2 x \cdot x + 1 x$

x^{2 + 1} + 2 x \cdot x + 1 x

$x^{2 + 1} + 2 x \cdot x + 1 x$

Step 1.2.2.1.2

Add

2

$2$ and

1

$1$ .

x^{3} + 2 x \cdot x + 1 x

$x^{3} + 2 x \cdot x + 1 x$

x^{3} + 2 x \cdot x + 1 x

$x^{3} + 2 x \cdot x + 1 x$

Step 1.2.2.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 1.2.2.2.1

Move

x

$x$ .

x^{3} + 2 (x \cdot x) + 1 x

$x^{3} + 2 (x \cdot x) + 1 x$

Step 1.2.2.2.2

Multiply

x

$x$ by

x

$x$ .

x^{3} + 2 x^{2} + 1 x

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

x^{3} + 2 x^{2} + 1 x

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

Step 1.2.2.3

Multiply

x

$x$ by

1

$1$ .

x^{3} + 2 x^{2} + x

$x^{3} + 2 x^{2} + x$

x^{3} + 2 x^{2} + x

$x^{3} + 2 x^{2} + x$

x^{3} + 2 x^{2} + x

$x^{3} + 2 x^{2} + x$

x^{3} + 2 x^{2} + x

$x^{3} + 2 x^{2} + x$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

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