Algebra Examples

$- 2 x^{2} (x - 5) + x (2 x^{2} - 10 x) + x$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 x^{2} x - 2 x^{2} \cdot - 5 + x (2 x^{2} - 10 x) + x$

Step 1.2

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

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Step 1.2.1

Move $x$ .

$- 2 (x \cdot x^{2}) - 2 x^{2} \cdot - 5 + x (2 x^{2} - 10 x) + x$

Step 1.2.2

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

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Step 1.2.2.1

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

$- 2 (x^{1} x^{2}) - 2 x^{2} \cdot - 5 + x (2 x^{2} - 10 x) + x$

Step 1.2.2.2

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

$- 2 x^{1 + 2} - 2 x^{2} \cdot - 5 + x (2 x^{2} - 10 x) + x$

Step 1.2.3

Add $1$ and $2$ .

$- 2 x^{3} - 2 x^{2} \cdot - 5 + x (2 x^{2} - 10 x) + x$

Step 1.3

Multiply $- 5$ by $- 2$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Rewrite using the commutative property of multiplication.

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

Step 1.6

Rewrite using the commutative property of multiplication.

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

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $x^{2}$ .

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

Step 1.7.1.2

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

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Step 1.7.1.2.1

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

$- 2 x^{3} + 10 x^{2} + 2 (x^{2} x^{1}) - 10 x \cdot x + x$

Step 1.7.1.2.2

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

$- 2 x^{3} + 10 x^{2} + 2 x^{2 + 1} - 10 x \cdot x + x$

Step 1.7.1.3

Add $2$ and $1$ .

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

Step 1.7.2

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

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Step 1.7.2.1

Move $x$ .

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

Step 1.7.2.2

Multiply $x$ by $x$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

Add $- 2 x^{3}$ and $2 x^{3}$ .

$10 x^{2} + 0 - 10 x^{2} + x$

Step 2.1.2

Add $10 x^{2}$ and $0$ .

$10 x^{2} - 10 x^{2} + x$

Step 2.1.3

Subtract $10 x^{2}$ from $10 x^{2}$ .

$0 + x$

Step 2.2

Add $0$ and $x$ .

$x$