Algebra Examples

${(x^{2} - 2)}^{2} + 2 (x^{2} - 2) - 8$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x^{2} - 2)}^{2}$ as $(x^{2} - 2) (x^{2} - 2)$ .

$(x^{2} - 2) (x^{2} - 2) + 2 (x^{2} - 2) - 8$

Step 1.2

Expand $(x^{2} - 2) (x^{2} - 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x^{2} (x^{2} - 2) - 2 (x^{2} - 2) + 2 (x^{2} - 2) - 8$

Step 1.2.2

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 2 - 2 (x^{2} - 2) + 2 (x^{2} - 2) - 8$

Step 1.2.3

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 2 - 2 x^{2} - 2 \cdot - 2 + 2 (x^{2} - 2) - 8$

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 $x^{2}$ by $x^{2}$ 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.

$x^{2 + 2} + x^{2} \cdot - 2 - 2 x^{2} - 2 \cdot - 2 + 2 (x^{2} - 2) - 8$

Step 1.3.1.1.2

Add $2$ and $2$ .

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

Step 1.3.1.2

Move $- 2$ to the left of $x^{2}$ .

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

Step 1.3.1.3

Multiply $- 2$ by $- 2$ .

$x^{4} - 2 x^{2} - 2 x^{2} + 4 + 2 (x^{2} - 2) - 8$

Step 1.3.2

Subtract $2 x^{2}$ from $- 2 x^{2}$ .

$x^{4} - 4 x^{2} + 4 + 2 (x^{2} - 2) - 8$

Step 1.4

Apply the distributive property.

$x^{4} - 4 x^{2} + 4 + 2 x^{2} + 2 \cdot - 2 - 8$

Step 1.5

Multiply $2$ by $- 2$ .

$x^{4} - 4 x^{2} + 4 + 2 x^{2} - 4 - 8$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $x^{4} - 4 x^{2} + 4 + 2 x^{2} - 4 - 8$ .

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Step 2.1.1

Subtract $4$ from $4$ .

$x^{4} - 4 x^{2} + 2 x^{2} + 0 - 8$

Step 2.1.2

Add $x^{4} - 4 x^{2} + 2 x^{2}$ and $0$ .

$x^{4} - 4 x^{2} + 2 x^{2} - 8$

Step 2.2

Add $- 4 x^{2}$ and $2 x^{2}$ .

$x^{4} - 2 x^{2} - 8$