Expand the Trigonometric Expression (8-3a^2)(2a^2+6)

$(8 - 3 a^{2}) (2 a^{2} + 6)$

Step 1

Expand $(8 - 3 a^{2}) (2 a^{2} + 6)$ using the FOIL Method.

Apply the distributive property.

$8 (2 a^{2} + 6) - 3 a^{2} (2 a^{2} + 6)$

Apply the distributive property.

$8 (2 a^{2}) + 8 \cdot 6 - 3 a^{2} (2 a^{2} + 6)$

Apply the distributive property.

$8 (2 a^{2}) + 8 \cdot 6 - 3 a^{2} (2 a^{2}) - 3 a^{2} \cdot 6$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $8$ .

$16 a^{2} + 8 \cdot 6 - 3 a^{2} (2 a^{2}) - 3 a^{2} \cdot 6$

Multiply $8$ by $6$ .

$16 a^{2} + 48 - 3 a^{2} (2 a^{2}) - 3 a^{2} \cdot 6$

Rewrite using the commutative property of multiplication.

$16 a^{2} + 48 - 3 \cdot 2 a^{2} a^{2} - 3 a^{2} \cdot 6$

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

Move $a^{2}$ .

$16 a^{2} + 48 - 3 \cdot 2 (a^{2} a^{2}) - 3 a^{2} \cdot 6$

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

$16 a^{2} + 48 - 3 \cdot 2 a^{2 + 2} - 3 a^{2} \cdot 6$

Add $2$ and $2$ .

$16 a^{2} + 48 - 3 \cdot 2 a^{4} - 3 a^{2} \cdot 6$

Multiply $- 3$ by $2$ .

$16 a^{2} + 48 - 6 a^{4} - 3 a^{2} \cdot 6$

Multiply $6$ by $- 3$ .

$16 a^{2} + 48 - 6 a^{4} - 18 a^{2}$

Subtract $18 a^{2}$ from $16 a^{2}$ .

$- 2 a^{2} + 48 - 6 a^{4}$