Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

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

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Step 3.1.1.1

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

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

Step 3.1.1.2

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

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

Step 3.1.2

Add $1$ and $2$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Move $3$ to the left of $x$ .

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

Step 4

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

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Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x$ .

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

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