Algebra Examples

$- 4 a^{2} (3 a^{2} - 4 a + 3)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Multiply $3$ by $- 4$ .

$- 4 \cdot 3 a^{2} a^{2} - 4 \cdot - 4 a^{2} a - 12 a^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $a^{2}$ .

$- 4 \cdot 3 (a^{2} a^{2}) - 4 \cdot - 4 a^{2} a - 12 a^{2}$

Step 3.1.2

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

$- 4 \cdot 3 a^{2 + 2} - 4 \cdot - 4 a^{2} a - 12 a^{2}$

Step 3.1.3

Add $2$ and $2$ .

$- 4 \cdot 3 a^{4} - 4 \cdot - 4 a^{2} a - 12 a^{2}$

Step 3.2

Multiply $- 4$ by $3$ .

$- 12 a^{4} - 4 \cdot - 4 a^{2} a - 12 a^{2}$

Step 3.3

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

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Step 3.3.1

Move $a$ .

$- 12 a^{4} - 4 \cdot - 4 (a \cdot a^{2}) - 12 a^{2}$

Step 3.3.2

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

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Step 3.3.2.1

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

$- 12 a^{4} - 4 \cdot - 4 (a^{1} a^{2}) - 12 a^{2}$

Step 3.3.2.2

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

$- 12 a^{4} - 4 \cdot - 4 a^{1 + 2} - 12 a^{2}$

Step 3.3.3

Add $1$ and $2$ .

$- 12 a^{4} - 4 \cdot - 4 a^{3} - 12 a^{2}$

Step 3.4

Multiply $- 4$ by $- 4$ .

$- 12 a^{4} + 16 a^{3} - 12 a^{2}$