Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Move $3$ to the left of $x^{2}$ .

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

Step 1.4

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

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Step 1.4.1

Move $x$ .

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

Step 1.4.2

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

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Step 1.4.2.1

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

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

Step 1.4.2.2

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

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

Step 1.4.3

Add $1$ and $2$ .

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

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Rewrite using the commutative property of multiplication.

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

Step 1.7

Rewrite using the commutative property of multiplication.

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

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $x^{2}$ .

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

Step 1.8.1.2

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

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Step 1.8.1.2.1

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

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

Step 1.8.1.2.2

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

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

Step 1.8.1.3

Add $2$ and $1$ .

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

Step 1.8.2

Multiply $2$ by $3$ .

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

Step 1.8.3

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

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Step 1.8.3.1

Move $x$ .

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

Step 1.8.3.2

Multiply $x$ by $x$ .

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

Step 1.8.4

Multiply $2$ by $5$ .

$2 x^{3} + 3 x^{2} + 6 x^{3} + 10 x^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 x^{3}$ and $6 x^{3}$ .

$8 x^{3} + 3 x^{2} + 10 x^{2}$

Step 2.2

Add $3 x^{2}$ and $10 x^{2}$ .

$8 x^{3} + 13 x^{2}$