Algebra Examples

$3 x^{3} (2 x^{2} - 4 x) + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x^{3} (2 x^{2}) + 3 x^{3} (- 4 x) + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{3} x^{2} + 3 x^{3} (- 4 x) + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.3

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{3} x^{2} + 3 \cdot - 4 x^{3} x + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x^{2}$ .

$3 \cdot 2 (x^{2} x^{3}) + 3 \cdot - 4 x^{3} x + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.1.2

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

$3 \cdot 2 x^{2 + 3} + 3 \cdot - 4 x^{3} x + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.1.3

Add $2$ and $3$ .

$3 \cdot 2 x^{5} + 3 \cdot - 4 x^{3} x + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.2

Multiply $3$ by $2$ .

$6 x^{5} + 3 \cdot - 4 x^{3} x + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.3

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

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Step 1.4.3.1

Move $x$ .

$6 x^{5} + 3 \cdot - 4 (x \cdot x^{3}) + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.3.2

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

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Step 1.4.3.2.1

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

$6 x^{5} + 3 \cdot - 4 (x^{1} x^{3}) + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.3.2.2

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

$6 x^{5} + 3 \cdot - 4 x^{1 + 3} + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.3.3

Add $1$ and $3$ .

$6 x^{5} + 3 \cdot - 4 x^{4} + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.4.4

Multiply $3$ by $- 4$ .

$6 x^{5} - 12 x^{4} + 2 x^{2} (4 x^{3} + 7 x^{2})$

Step 1.5

Apply the distributive property.

$6 x^{5} - 12 x^{4} + 2 x^{2} (4 x^{3}) + 2 x^{2} (7 x^{2})$

Step 1.6

Rewrite using the commutative property of multiplication.

$6 x^{5} - 12 x^{4} + 2 \cdot 4 x^{2} x^{3} + 2 x^{2} (7 x^{2})$

Step 1.7

Rewrite using the commutative property of multiplication.

$6 x^{5} - 12 x^{4} + 2 \cdot 4 x^{2} x^{3} + 2 \cdot 7 x^{2} x^{2}$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $x^{3}$ .

$6 x^{5} - 12 x^{4} + 2 \cdot 4 (x^{3} x^{2}) + 2 \cdot 7 x^{2} x^{2}$

Step 1.8.1.2

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

$6 x^{5} - 12 x^{4} + 2 \cdot 4 x^{3 + 2} + 2 \cdot 7 x^{2} x^{2}$

Step 1.8.1.3

Add $3$ and $2$ .

$6 x^{5} - 12 x^{4} + 2 \cdot 4 x^{5} + 2 \cdot 7 x^{2} x^{2}$

Step 1.8.2

Multiply $2$ by $4$ .

$6 x^{5} - 12 x^{4} + 8 x^{5} + 2 \cdot 7 x^{2} x^{2}$

Step 1.8.3

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

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Step 1.8.3.1

Move $x^{2}$ .

$6 x^{5} - 12 x^{4} + 8 x^{5} + 2 \cdot 7 (x^{2} x^{2})$

Step 1.8.3.2

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

$6 x^{5} - 12 x^{4} + 8 x^{5} + 2 \cdot 7 x^{2 + 2}$

Step 1.8.3.3

Add $2$ and $2$ .

$6 x^{5} - 12 x^{4} + 8 x^{5} + 2 \cdot 7 x^{4}$

Step 1.8.4

Multiply $2$ by $7$ .

$6 x^{5} - 12 x^{4} + 8 x^{5} + 14 x^{4}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 x^{5}$ and $8 x^{5}$ .

$14 x^{5} - 12 x^{4} + 14 x^{4}$

Step 2.2

Add $- 12 x^{4}$ and $14 x^{4}$ .

$14 x^{5} + 2 x^{4}$