Expand the Trigonometric Expression (x^2+4)(x^2-6)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

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

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

Multiply $4$ by $- 6$ .

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

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

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