Algebra Examples

$a^{4} - 81 - {(a^{2} + 9)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(a^{2} + 9)}^{2}$ as $(a^{2} + 9) (a^{2} + 9)$ .

$a^{4} - 81 - ((a^{2} + 9) (a^{2} + 9))$

Step 1.2

Expand $(a^{2} + 9) (a^{2} + 9)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$a^{4} - 81 - (a^{2} (a^{2} + 9) + 9 (a^{2} + 9))$

Step 1.2.2

Apply the distributive property.

$a^{4} - 81 - (a^{2} a^{2} + a^{2} \cdot 9 + 9 (a^{2} + 9))$

Step 1.2.3

Apply the distributive property.

$a^{4} - 81 - (a^{2} a^{2} + a^{2} \cdot 9 + 9 a^{2} + 9 \cdot 9)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

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

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Step 1.3.1.1.1

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

$a^{4} - 81 - (a^{2 + 2} + a^{2} \cdot 9 + 9 a^{2} + 9 \cdot 9)$

Step 1.3.1.1.2

Add $2$ and $2$ .

$a^{4} - 81 - (a^{4} + a^{2} \cdot 9 + 9 a^{2} + 9 \cdot 9)$

Step 1.3.1.2

Move $9$ to the left of $a^{2}$ .

$a^{4} - 81 - (a^{4} + 9 \cdot a^{2} + 9 a^{2} + 9 \cdot 9)$

Step 1.3.1.3

Multiply $9$ by $9$ .

$a^{4} - 81 - (a^{4} + 9 a^{2} + 9 a^{2} + 81)$

Step 1.3.2

Add $9 a^{2}$ and $9 a^{2}$ .

$a^{4} - 81 - (a^{4} + 18 a^{2} + 81)$

Step 1.4

Apply the distributive property.

$a^{4} - 81 - a^{4} - (18 a^{2}) - 1 \cdot 81$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $18$ by $- 1$ .

$a^{4} - 81 - a^{4} - 18 a^{2} - 1 \cdot 81$

Step 1.5.2

Multiply $- 1$ by $81$ .

$a^{4} - 81 - a^{4} - 18 a^{2} - 81$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $a^{4} - 81 - a^{4} - 18 a^{2} - 81$ .

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Step 2.1.1

Subtract $a^{4}$ from $a^{4}$ .

$0 - 81 - 18 a^{2} - 81$

Step 2.1.2

Subtract $81$ from $0$ .

$- 81 - 18 a^{2} - 81$

Step 2.2

Subtract $81$ from $- 81$ .

$- 18 a^{2} - 162$