Algebra Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Move $5$ to the left of $x^{2}$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $2$ .

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

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