Algebra Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $2$ .

$6 x^{2} y + 3 \cdot 5 x^{2} x$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$6 x^{2} y + 3 \cdot 5 (x \cdot x^{2})$

Step 2.2.2

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

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Step 2.2.2.1

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

$6 x^{2} y + 3 \cdot 5 (x^{1} x^{2})$

Step 2.2.2.2

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

$6 x^{2} y + 3 \cdot 5 x^{1 + 2}$

Step 2.2.3

Add $1$ and $2$ .

$6 x^{2} y + 3 \cdot 5 x^{3}$

Step 2.3

Multiply $3$ by $5$ .

$6 x^{2} y + 15 x^{3}$