Expand the Trigonometric Expression -5g^2(g^2-4g)

$- 5 g^{2} (g^{2} - 4 g)$

Step 1

Apply the distributive property.

$- 5 g^{2} g^{2} - 5 g^{2} (- 4 g)$

Step 2

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

Move $g^{2}$ .

$- 5 (g^{2} g^{2}) - 5 g^{2} (- 4 g)$

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

$- 5 g^{2 + 2} - 5 g^{2} (- 4 g)$

Add $2$ and $2$ .

$- 5 g^{4} - 5 g^{2} (- 4 g)$

Step 3

Rewrite using the commutative property of multiplication.

$- 5 g^{4} - 5 \cdot - 4 g^{2} g$

Step 4

Simplify each term.

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

Move $g$ .

$- 5 g^{4} - 5 \cdot - 4 (g \cdot g^{2})$

Multiply $g$ by $g^{2}$ .

Raise $g$ to the power of $1$ .

$- 5 g^{4} - 5 \cdot - 4 (g^{1} g^{2})$

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

$- 5 g^{4} - 5 \cdot - 4 g^{1 + 2}$

Add $1$ and $2$ .

$- 5 g^{4} - 5 \cdot - 4 g^{3}$

Multiply $- 5$ by $- 4$ .

$- 5 g^{4} + 20 g^{3}$