Pre-Algebra Examples

(x^{2} + 2 x) (x + 10)

$(x^{2} + 2 x) (x + 10)$

Step 1

Expand

(x^{2} + 2 x) (x + 10)

$(x^{2} + 2 x) (x + 10)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

x^{2} (x + 10) + 2 x (x + 10)

$x^{2} (x + 10) + 2 x (x + 10)$

Step 1.2

Apply the distributive property.

x^{2} x + x^{2} \cdot 10 + 2 x (x + 10)

$x^{2} x + x^{2} \cdot 10 + 2 x (x + 10)$

Step 1.3

Apply the distributive property.

x^{2} x + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{2} x + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

x^{2} x + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{2} x + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 2.1.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ .

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Step 2.1.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

x^{2} x^{1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{2} x^{1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

Step 2.1.1.1.2

Use the power rule

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

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

x^{2 + 1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{2 + 1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

x^{2 + 1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{2 + 1} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

Step 2.1.1.2

Add

2

$2$ and

1

$1$ .

x^{3} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{3} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

x^{3} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10

$x^{3} + x^{2} \cdot 10 + 2 x \cdot x + 2 x \cdot 10$

Step 2.1.2

Move

10

$10$ to the left of

x^{2}

$x^{2}$ .

x^{3} + 10 \cdot x^{2} + 2 x \cdot x + 2 x \cdot 10

$x^{3} + 10 \cdot x^{2} + 2 x \cdot x + 2 x \cdot 10$

Step 2.1.3

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.3.1

Move

x

$x$ .

x^{3} + 10 x^{2} + 2 (x \cdot x) + 2 x \cdot 10

$x^{3} + 10 x^{2} + 2 (x \cdot x) + 2 x \cdot 10$

Step 2.1.3.2

Multiply

x

$x$ by

x

$x$ .

x^{3} + 10 x^{2} + 2 x^{2} + 2 x \cdot 10

$x^{3} + 10 x^{2} + 2 x^{2} + 2 x \cdot 10$

x^{3} + 10 x^{2} + 2 x^{2} + 2 x \cdot 10

$x^{3} + 10 x^{2} + 2 x^{2} + 2 x \cdot 10$

Step 2.1.4

Multiply

10

$10$ by

2

$2$ .

x^{3} + 10 x^{2} + 2 x^{2} + 20 x

$x^{3} + 10 x^{2} + 2 x^{2} + 20 x$

x^{3} + 10 x^{2} + 2 x^{2} + 20 x

$x^{3} + 10 x^{2} + 2 x^{2} + 20 x$

Step 2.2

Add

10 x^{2}

$10 x^{2}$ and

2 x^{2}

$2 x^{2}$ .

x^{3} + 12 x^{2} + 20 x

$x^{3} + 12 x^{2} + 20 x$

x^{3} + 12 x^{2} + 20 x

$x^{3} + 12 x^{2} + 20 x$

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