Algebra Examples

$x^{4} + x$ , $- x + 6$

Step 1

Multiply the expressions.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify each term.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 3.2.1

Move $x$ .

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

Step 3.2.2

Multiply $x$ by $x^{4}$ .

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Step 3.2.2.1

Raise $x$ to the power of $1$ .

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

Step 3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.2.3

Add $1$ and $4$ .

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

Step 3.3

Move $6$ to the left of $x^{4}$ .

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

Step 3.4

Rewrite using the commutative property of multiplication.

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

Step 3.5

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

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Step 3.5.1

Move $x$ .

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

Step 3.5.2

Multiply $x$ by $x$ .

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

Step 3.6

Move $6$ to the left of $x$ .

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

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