Algebra Examples

$3 x \cdot x^{4} + 3 x \cdot x^{3} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Move $x^{4}$ .

$3 (x^{4} x) + 3 x \cdot x^{3} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.1.2

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

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Step 1.1.2.1

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

$3 (x^{4} x^{1}) + 3 x \cdot x^{3} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.1.2.2

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

$3 x^{4 + 1} + 3 x \cdot x^{3} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.1.3

Add $4$ and $1$ .

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

Step 1.2

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 1.2.1

Move $x^{3}$ .

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

Step 1.2.2

Multiply $x^{3}$ by $x$ .

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Step 1.2.2.1

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

$3 x^{5} + 3 (x^{3} x^{1}) - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.2.2.2

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

$3 x^{5} + 3 x^{3 + 1} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.2.3

Add $3$ and $1$ .

$3 x^{5} + 3 x^{4} - 5 x^{2} x^{3} - 5 x^{2} x$

Step 1.3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.3.1

Move $x^{3}$ .

$3 x^{5} + 3 x^{4} - 5 (x^{3} x^{2}) - 5 x^{2} x$

Step 1.3.2

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

$3 x^{5} + 3 x^{4} - 5 x^{3 + 2} - 5 x^{2} x$

Step 1.3.3

Add $3$ and $2$ .

$3 x^{5} + 3 x^{4} - 5 x^{5} - 5 x^{2} x$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$3 x^{5} + 3 x^{4} - 5 x^{5} - 5 (x \cdot x^{2})$

Step 1.4.2

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

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Step 1.4.2.1

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

$3 x^{5} + 3 x^{4} - 5 x^{5} - 5 (x^{1} x^{2})$

Step 1.4.2.2

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

$3 x^{5} + 3 x^{4} - 5 x^{5} - 5 x^{1 + 2}$

Step 1.4.3

Add $1$ and $2$ .

$3 x^{5} + 3 x^{4} - 5 x^{5} - 5 x^{3}$

Step 2

Subtract $5 x^{5}$ from $3 x^{5}$ .

$- 2 x^{5} + 3 x^{4} - 5 x^{3}$