Examples

x^{4} + x

$x^{4} + x$ ,

- x + 6

$- x + 6$

Step 1

Multiply the expressions.

(x^{4} + x) \cdot (- x + 6)

$(x^{4} + x) \cdot (- x + 6)$

Step 2

Expand

(x^{4} + x) (- x + 6)

$(x^{4} + x) (- x + 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

x^{4} (- x + 6) + x (- x + 6)

$x^{4} (- x + 6) + x (- x + 6)$

Step 2.2

Apply the distributive property.

x^{4} (- x) + x^{4} \cdot 6 + x (- x + 6)

$x^{4} (- x) + x^{4} \cdot 6 + x (- x + 6)$

Step 2.3

Apply the distributive property.

x^{4} (- x) + x^{4} \cdot 6 + x (- x) + x \cdot 6

$x^{4} (- x) + x^{4} \cdot 6 + x (- x) + x \cdot 6$

x^{4} (- x) + x^{4} \cdot 6 + x (- x) + x \cdot 6

$x^{4} (- x) + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3

Simplify each term.

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Step 3.1

Rewrite using the commutative property of multiplication.

- x^{4} x + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- x^{4} x + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3.2

Multiply

x^{4}

$x^{4}$ by

x

$x$ by adding the exponents.

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Step 3.2.1

Move

x

$x$ .

- (x \cdot x^{4}) + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- (x \cdot x^{4}) + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3.2.2

Multiply

x

$x$ by

x^{4}

$x^{4}$ .

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Step 3.2.2.1

Raise

x

$x$ to the power of

1

$1$ .

- (x^{1} x^{4}) + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- (x^{1} x^{4}) + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3.2.2.2

Use the power rule

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

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

- x^{1 + 4} + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- x^{1 + 4} + x^{4} \cdot 6 + x (- x) + x \cdot 6$

- x^{1 + 4} + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- x^{1 + 4} + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3.2.3

Add

1

$1$ and

4

$4$ .

- x^{5} + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- x^{5} + x^{4} \cdot 6 + x (- x) + x \cdot 6$

- x^{5} + x^{4} \cdot 6 + x (- x) + x \cdot 6

$- x^{5} + x^{4} \cdot 6 + x (- x) + x \cdot 6$

Step 3.3

Move

6

$6$ to the left of

x^{4}

$x^{4}$ .

- x^{5} + 6 \cdot x^{4} + x (- x) + x \cdot 6

$- x^{5} + 6 \cdot x^{4} + x (- x) + x \cdot 6$

Step 3.4

Rewrite using the commutative property of multiplication.

- x^{5} + 6 x^{4} - x \cdot x + x \cdot 6

$- x^{5} + 6 x^{4} - x \cdot x + x \cdot 6$

Step 3.5

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 3.5.1

Move

x

$x$ .

- x^{5} + 6 x^{4} - (x \cdot x) + x \cdot 6

$- x^{5} + 6 x^{4} - (x \cdot x) + x \cdot 6$

Step 3.5.2

Multiply

x

$x$ by

x

$x$ .

- x^{5} + 6 x^{4} - x^{2} + x \cdot 6

$- x^{5} + 6 x^{4} - x^{2} + x \cdot 6$

- x^{5} + 6 x^{4} - x^{2} + x \cdot 6

$- x^{5} + 6 x^{4} - x^{2} + x \cdot 6$

Step 3.6

Move

6

$6$ to the left of

x

$x$ .

- x^{5} + 6 x^{4} - x^{2} + 6 x

$- x^{5} + 6 x^{4} - x^{2} + 6 x$

- x^{5} + 6 x^{4} - x^{2} + 6 x

$- x^{5} + 6 x^{4} - x^{2} + 6 x$

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