Basic Math Examples

$- a^{2} (9 a^{2} + 4) + 8 a^{4}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- a^{2} (9 a^{2}) - a^{2} \cdot 4 + 8 a^{4}$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 1 \cdot 9 a^{2} a^{2} - a^{2} \cdot 4 + 8 a^{4}$

Step 1.3

Multiply $4$ by $- 1$ .

$- 1 \cdot 9 a^{2} a^{2} - 4 a^{2} + 8 a^{4}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $a^{2}$ .

$- 1 \cdot 9 (a^{2} a^{2}) - 4 a^{2} + 8 a^{4}$

Step 1.4.1.2

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

$- 1 \cdot 9 a^{2 + 2} - 4 a^{2} + 8 a^{4}$

Step 1.4.1.3

Add $2$ and $2$ .

$- 1 \cdot 9 a^{4} - 4 a^{2} + 8 a^{4}$

Step 1.4.2

Multiply $- 1$ by $9$ .

$- 9 a^{4} - 4 a^{2} + 8 a^{4}$

Step 2

Add $- 9 a^{4}$ and $8 a^{4}$ .

$- a^{4} - 4 a^{2}$