Algebra Examples

$(x^{2} + 10 x + 100) (x - 10)$

Step 1

Expand $(x^{2} + 10 x + 100) (x - 10)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 10 + 10 x \cdot x + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 10 + 10 x \cdot x + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 10 + 10 x \cdot x + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 10 + 10 x \cdot x + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.2

Move $- 10$ to the left of $x^{2}$ .

$x^{3} - 10 \cdot x^{2} + 10 x \cdot x + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$x^{3} - 10 x^{2} + 10 (x \cdot x) + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 10 x^{2} + 10 x^{2} + 10 x \cdot - 10 + 100 x + 100 \cdot - 10$

Step 2.1.4

Multiply $- 10$ by $10$ .

$x^{3} - 10 x^{2} + 10 x^{2} - 100 x + 100 x + 100 \cdot - 10$

Step 2.1.5

Multiply $100$ by $- 10$ .

$x^{3} - 10 x^{2} + 10 x^{2} - 100 x + 100 x - 1000$

Step 2.2

Combine the opposite terms in $x^{3} - 10 x^{2} + 10 x^{2} - 100 x + 100 x - 1000$ .

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Step 2.2.1

Add $- 10 x^{2}$ and $10 x^{2}$ .

$x^{3} + 0 - 100 x + 100 x - 1000$

Step 2.2.2

Add $x^{3}$ and $0$ .

$x^{3} - 100 x + 100 x - 1000$

Step 2.2.3

Add $- 100 x$ and $100 x$ .

$x^{3} + 0 - 1000$

Step 2.2.4

Add $x^{3}$ and $0$ .

$x^{3} - 1000$