Algebra Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$- 3 \cdot 7 a \cdot a^{2} - 3 a \cdot - 4$

Step 1.2.2

Multiply $- 4$ by $- 3$ .

$- 3 \cdot 7 a \cdot a^{2} + 12 a$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $a^{2}$ .

$- 3 \cdot 7 (a^{2} a) + 12 a$

Step 2.1.2

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

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Step 2.1.2.1

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

$- 3 \cdot 7 (a^{2} a^{1}) + 12 a$

Step 2.1.2.2

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

$- 3 \cdot 7 a^{2 + 1} + 12 a$

Step 2.1.3

Add $2$ and $1$ .

$- 3 \cdot 7 a^{3} + 12 a$

Step 2.2

Multiply $- 3$ by $7$ .

$- 21 a^{3} + 12 a$