Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(x^{2} + 4) (x^{2} - 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

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

Step 3.1.1.2

Add $2$ and $2$ .

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

Step 3.1.2

Move $- 6$ to the left of $x^{2}$ .

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

Step 3.1.3

Multiply $4$ by $- 6$ .

$x^{4} - 6 x^{2} + 4 x^{2} - 24$

Step 3.2

Add $- 6 x^{2}$ and $4 x^{2}$ .

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