Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.2

Add $2$ and $1$ .

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

Step 4

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

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Step 4.1

Move $x^{2}$ .

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

Step 4.2

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

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

Step 4.3

Add $2$ and $2$ .

$10 x^{4} + x^{3}$