Precalculus Examples

$(x^{2} + 6) (x^{2} - 2) (2)$

Step 1

Expand $(x^{2} + 6) (x^{2} - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(x^{2} (x^{2} - 2) + 6 (x^{2} - 2)) \cdot 2$

Step 1.2

Apply the distributive property.

$(x^{2} x^{2} + x^{2} \cdot - 2 + 6 (x^{2} - 2)) \cdot 2$

Step 1.3

Apply the distributive property.

$(x^{2} x^{2} + x^{2} \cdot - 2 + 6 x^{2} + 6 \cdot - 2) \cdot 2$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

$(x^{2 + 2} + x^{2} \cdot - 2 + 6 x^{2} + 6 \cdot - 2) \cdot 2$

Step 2.1.1.2

Add $2$ and $2$ .

$(x^{4} + x^{2} \cdot - 2 + 6 x^{2} + 6 \cdot - 2) \cdot 2$

Step 2.1.2

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

$(x^{4} - 2 \cdot x^{2} + 6 x^{2} + 6 \cdot - 2) \cdot 2$

Step 2.1.3

Multiply $6$ by $- 2$ .

$(x^{4} - 2 x^{2} + 6 x^{2} - 12) \cdot 2$

Step 2.2

Add $- 2 x^{2}$ and $6 x^{2}$ .

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

Step 3

Apply the distributive property.

$x^{4} \cdot 2 + 4 x^{2} \cdot 2 - 12 \cdot 2$

Step 4

Simplify.

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Step 4.1

Move $2$ to the left of $x^{4}$ .

$2 \cdot x^{4} + 4 x^{2} \cdot 2 - 12 \cdot 2$

Step 4.2

Multiply $2$ by $4$ .

$2 \cdot x^{4} + 8 x^{2} - 12 \cdot 2$

Step 4.3

Multiply $- 12$ by $2$ .

$2 \cdot x^{4} + 8 x^{2} - 24$

$2 x^{4} + 8 x^{2} - 24$