Expand the Trigonometric Expression 2x^2(9x^2-16)

$2 x^{2} (9 x^{2} - 16)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$2 x^{2} (9 x^{2}) + 2 x^{2} \cdot - 16$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 \cdot 9 x^{2} x^{2} + 2 x^{2} \cdot - 16$

Multiply $- 16$ by $2$ .

$2 \cdot 9 x^{2} x^{2} - 32 x^{2}$

Step 2

Simplify each term.

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

Move $x^{2}$ .

$2 \cdot 9 (x^{2} x^{2}) - 32 x^{2}$

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

$2 \cdot 9 x^{2 + 2} - 32 x^{2}$

Add $2$ and $2$ .

$2 \cdot 9 x^{4} - 32 x^{2}$

Multiply $2$ by $9$ .

$18 x^{4} - 32 x^{2}$