Algebra Examples

f (x) = x^{2}

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

g (x) = 4 x - 1

$g (x) = 4 x - 1$

Step 1

Replace the function designators with the actual functions in

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

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

(x^{2}) \cdot (4 x - 1)

$(x^{2}) \cdot (4 x - 1)$

Step 2

Simplify.

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

x^{2} (4 x) + x^{2} \cdot - 1

$x^{2} (4 x) + x^{2} \cdot - 1$

Step 2.1.2

Reorder.

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Step 2.1.2.1

Rewrite using the commutative property of multiplication.

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

$4 x^{2} x + x^{2} \cdot - 1$

Step 2.1.2.2

Move

- 1

$- 1$ to the left of

x^{2}

$x^{2}$ .

4 x^{2} x - 1 \cdot x^{2}

$4 x^{2} x - 1 \cdot x^{2}$

4 x^{2} x - 1 \cdot x^{2}

$4 x^{2} x - 1 \cdot x^{2}$

4 x^{2} x - 1 \cdot x^{2}

$4 x^{2} x - 1 \cdot x^{2}$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 2.2.1.1

Move

x

$x$ .

4 (x \cdot x^{2}) - 1 \cdot x^{2}

$4 (x \cdot x^{2}) - 1 \cdot x^{2}$

Step 2.2.1.2

Multiply

x

$x$ by

x^{2}

$x^{2}$ .

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Step 2.2.1.2.1

Raise

x

$x$ to the power of

1

$1$ .

4 (x^{1} x^{2}) - 1 \cdot x^{2}

$4 (x^{1} x^{2}) - 1 \cdot x^{2}$

Step 2.2.1.2.2

Use the power rule

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

$4 x^{1 + 2} - 1 \cdot x^{2}$

Step 2.2.1.3

Add

$1$ and

$2$ .

$4 x^{3} - 1 \cdot x^{2}$

Step 2.2.2

Rewrite

$- 1 x^{2}$ as

$- x^{2}$ .

$4 x^{3} - x^{2}$

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