Algebra Examples

$4 x^{2} (3 x^{3} + 6 x - 3) + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 x^{2} (3 x^{3}) + 4 x^{2} (6 x) + 4 x^{2} \cdot - 3 + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x^{2} x^{3} + 4 x^{2} (6 x) + 4 x^{2} \cdot - 3 + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x^{2} x^{3} + 4 \cdot 6 x^{2} x + 4 x^{2} \cdot - 3 + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.2.3

Multiply $- 3$ by $4$ .

$4 \cdot 3 x^{2} x^{3} + 4 \cdot 6 x^{2} x - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.3.1.1

Move $x^{3}$ .

$4 \cdot 3 (x^{3} x^{2}) + 4 \cdot 6 x^{2} x - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.1.2

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

$4 \cdot 3 x^{3 + 2} + 4 \cdot 6 x^{2} x - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.1.3

Add $3$ and $2$ .

$4 \cdot 3 x^{5} + 4 \cdot 6 x^{2} x - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.2

Multiply $4$ by $3$ .

$12 x^{5} + 4 \cdot 6 x^{2} x - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.3

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

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Step 1.3.3.1

Move $x$ .

$12 x^{5} + 4 \cdot 6 (x \cdot x^{2}) - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.3.2

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

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Step 1.3.3.2.1

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

$12 x^{5} + 4 \cdot 6 (x^{1} x^{2}) - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.3.2.2

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

$12 x^{5} + 4 \cdot 6 x^{1 + 2} - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.3.3

Add $1$ and $2$ .

$12 x^{5} + 4 \cdot 6 x^{3} - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.3.4

Multiply $4$ by $6$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 x^{3} (2 x^{2} - 5 x + 1)$

Step 1.4

Apply the distributive property.

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 x^{3} (2 x^{2}) + 3 x^{3} (- 5 x) + 3 x^{3} \cdot 1$

Step 1.5

Simplify.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 x^{3} x^{2} + 3 x^{3} (- 5 x) + 3 x^{3} \cdot 1$

Step 1.5.2

Rewrite using the commutative property of multiplication.

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 x^{3} x^{2} + 3 \cdot - 5 x^{3} x + 3 x^{3} \cdot 1$

Step 1.5.3

Multiply $3$ by $1$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 x^{3} x^{2} + 3 \cdot - 5 x^{3} x + 3 x^{3}$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 1.6.1.1

Move $x^{2}$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 (x^{2} x^{3}) + 3 \cdot - 5 x^{3} x + 3 x^{3}$

Step 1.6.1.2

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

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 x^{2 + 3} + 3 \cdot - 5 x^{3} x + 3 x^{3}$

Step 1.6.1.3

Add $2$ and $3$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 3 \cdot 2 x^{5} + 3 \cdot - 5 x^{3} x + 3 x^{3}$

Step 1.6.2

Multiply $3$ by $2$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} + 3 \cdot - 5 x^{3} x + 3 x^{3}$

Step 1.6.3

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 1.6.3.1

Move $x$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} + 3 \cdot - 5 (x \cdot x^{3}) + 3 x^{3}$

Step 1.6.3.2

Multiply $x$ by $x^{3}$ .

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Step 1.6.3.2.1

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

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} + 3 \cdot - 5 (x^{1} x^{3}) + 3 x^{3}$

Step 1.6.3.2.2

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

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} + 3 \cdot - 5 x^{1 + 3} + 3 x^{3}$

Step 1.6.3.3

Add $1$ and $3$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} + 3 \cdot - 5 x^{4} + 3 x^{3}$

Step 1.6.4

Multiply $3$ by $- 5$ .

$12 x^{5} + 24 x^{3} - 12 x^{2} + 6 x^{5} - 15 x^{4} + 3 x^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $12 x^{5}$ and $6 x^{5}$ .

$18 x^{5} + 24 x^{3} - 12 x^{2} - 15 x^{4} + 3 x^{3}$

Step 2.2

Add $24 x^{3}$ and $3 x^{3}$ .

$18 x^{5} + 27 x^{3} - 12 x^{2} - 15 x^{4}$

Step 2.3

Reorder.

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Step 2.3.1

Move $- 12 x^{2}$ .

$18 x^{5} + 27 x^{3} - 15 x^{4} - 12 x^{2}$

Step 2.3.2

Move $27 x^{3}$ .

$18 x^{5} - 15 x^{4} + 27 x^{3} - 12 x^{2}$