Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Multiply $7$ by $- 3$ .

$- 3 \cdot 2 x^{2} x - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x$ .

$- 3 \cdot 2 (x \cdot x^{2}) - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$- 3 \cdot 2 (x^{1} x^{2}) - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.4.1.2.2

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

$- 3 \cdot 2 x^{1 + 2} - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.4.1.3

Add $1$ and $2$ .

$- 3 \cdot 2 x^{3} - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.4.2

Multiply $- 3$ by $2$ .

$- 6 x^{3} - 21 x^{2} + 4 x (3 x^{2} - x + 5) + 2 (x^{2} - 4)$

Step 1.5

Apply the distributive property.

$- 6 x^{3} - 21 x^{2} + 4 x (3 x^{2}) + 4 x (- x) + 4 x \cdot 5 + 2 (x^{2} - 4)$

Step 1.6

Simplify.

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Step 1.6.1

Rewrite using the commutative property of multiplication.

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 x \cdot x^{2} + 4 x (- x) + 4 x \cdot 5 + 2 (x^{2} - 4)$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 x \cdot x^{2} + 4 \cdot - 1 x \cdot x + 4 x \cdot 5 + 2 (x^{2} - 4)$

Step 1.6.3

Multiply $5$ by $4$ .

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 x \cdot x^{2} + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $x^{2}$ .

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 (x^{2} x) + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7.1.2

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

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Step 1.7.1.2.1

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

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 (x^{2} x^{1}) + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7.1.2.2

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

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 x^{2 + 1} + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7.1.3

Add $2$ and $1$ .

$- 6 x^{3} - 21 x^{2} + 4 \cdot 3 x^{3} + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7.2

Multiply $4$ by $3$ .

$- 6 x^{3} - 21 x^{2} + 12 x^{3} + 4 \cdot - 1 x \cdot x + 20 x + 2 (x^{2} - 4)$

Step 1.7.3

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

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Step 1.7.3.1

Move $x$ .

$- 6 x^{3} - 21 x^{2} + 12 x^{3} + 4 \cdot - 1 (x \cdot x) + 20 x + 2 (x^{2} - 4)$

Step 1.7.3.2

Multiply $x$ by $x$ .

$- 6 x^{3} - 21 x^{2} + 12 x^{3} + 4 \cdot - 1 x^{2} + 20 x + 2 (x^{2} - 4)$

Step 1.7.4

Multiply $4$ by $- 1$ .

$- 6 x^{3} - 21 x^{2} + 12 x^{3} - 4 x^{2} + 20 x + 2 (x^{2} - 4)$

Step 1.8

Apply the distributive property.

$- 6 x^{3} - 21 x^{2} + 12 x^{3} - 4 x^{2} + 20 x + 2 x^{2} + 2 \cdot - 4$

Step 1.9

Multiply $2$ by $- 4$ .

$- 6 x^{3} - 21 x^{2} + 12 x^{3} - 4 x^{2} + 20 x + 2 x^{2} - 8$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 6 x^{3}$ and $12 x^{3}$ .

$6 x^{3} - 21 x^{2} - 4 x^{2} + 20 x + 2 x^{2} - 8$

Step 2.2

Subtract $4 x^{2}$ from $- 21 x^{2}$ .

$6 x^{3} - 25 x^{2} + 20 x + 2 x^{2} - 8$

Step 2.3

Add $- 25 x^{2}$ and $2 x^{2}$ .

$6 x^{3} - 23 x^{2} + 20 x - 8$