Pre-Algebra Examples

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

Step 1

Multiply the expressions.

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

Step 2

Expand $(x^{2} + 5 x) (x - 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x^{2} (x - 6) + 5 x (x - 6)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.1.1.1

Multiply $x^{2}$ by $x$ .

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Step 3.1.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 6 + 5 x \cdot x + 5 x \cdot - 6$

Step 3.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 6 + 5 x \cdot x + 5 x \cdot - 6$

Step 3.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 6 + 5 x \cdot x + 5 x \cdot - 6$

Step 3.1.2

Move $- 6$ to the left of $x^{2}$ .

$x^{3} - 6 \cdot x^{2} + 5 x \cdot x + 5 x \cdot - 6$

Step 3.1.3

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

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Step 3.1.3.1

Move $x$ .

$x^{3} - 6 x^{2} + 5 (x \cdot x) + 5 x \cdot - 6$

Step 3.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 6 x^{2} + 5 x^{2} + 5 x \cdot - 6$

Step 3.1.4

Multiply $- 6$ by $5$ .

$x^{3} - 6 x^{2} + 5 x^{2} - 30 x$

Step 3.2

Add $- 6 x^{2}$ and $5 x^{2}$ .

$x^{3} - x^{2} - 30 x$

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