Basic Math Examples

$- A^{2} (- 2 A^{2} + 3 A - 2)$

Step 1

Apply the distributive property.

$- A^{2} (- 2 A^{2}) - A^{2} (3 A) - A^{2} \cdot - 2$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 2 A^{2} A^{2} - A^{2} (3 A) - A^{2} \cdot - 2$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 2 A^{2} A^{2} - 1 \cdot 3 A^{2} A - A^{2} \cdot - 2$

Step 2.3

Multiply $- 2$ by $- 1$ .

$- 1 \cdot - 2 A^{2} A^{2} - 1 \cdot 3 A^{2} A + 2 A^{2}$

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 $A^{2}$ .

$- 1 \cdot - 2 (A^{2} A^{2}) - 1 \cdot 3 A^{2} A + 2 A^{2}$

Step 3.1.2

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

$- 1 \cdot - 2 A^{2 + 2} - 1 \cdot 3 A^{2} A + 2 A^{2}$

Step 3.1.3

Add $2$ and $2$ .

$- 1 \cdot - 2 A^{4} - 1 \cdot 3 A^{2} A + 2 A^{2}$

Step 3.2

Multiply $- 1$ by $- 2$ .

$2 A^{4} - 1 \cdot 3 A^{2} A + 2 A^{2}$

Step 3.3

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

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Step 3.3.1

Move $A$ .

$2 A^{4} - 1 \cdot 3 (A \cdot A^{2}) + 2 A^{2}$

Step 3.3.2

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

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Step 3.3.2.1

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

$2 A^{4} - 1 \cdot 3 (A^{1} A^{2}) + 2 A^{2}$

Step 3.3.2.2

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

$2 A^{4} - 1 \cdot 3 A^{1 + 2} + 2 A^{2}$

Step 3.3.3

Add $1$ and $2$ .

$2 A^{4} - 1 \cdot 3 A^{3} + 2 A^{2}$

Step 3.4

Multiply $- 1$ by $3$ .

$2 A^{4} - 3 A^{3} + 2 A^{2}$