Simplify -t(-4t^3+8t^2)

$- t (- 4 t^{3} + 8 t^{2})$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$- t (- 4 t^{3}) - t (8 t^{2})$

Reorder.

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 4 t \cdot t^{3} - t (8 t^{2})$

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 4 t \cdot t^{3} - 1 \cdot 8 t \cdot t^{2}$

Step 2

Simplify each term.

Multiply $t$ by $t^{3}$ by adding the exponents.

Move $t^{3}$ .

$- 1 \cdot - 4 (t^{3} t) - 1 \cdot 8 t \cdot t^{2}$

Multiply $t^{3}$ by $t$ .

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

$- 1 \cdot - 4 (t^{3} t^{1}) - 1 \cdot 8 t \cdot t^{2}$

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

$- 1 \cdot - 4 t^{3 + 1} - 1 \cdot 8 t \cdot t^{2}$

Add $3$ and $1$ .

$- 1 \cdot - 4 t^{4} - 1 \cdot 8 t \cdot t^{2}$

Multiply $- 1$ by $- 4$ .

$4 t^{4} - 1 \cdot 8 t \cdot t^{2}$

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

Move $t^{2}$ .

$4 t^{4} - 1 \cdot 8 (t^{2} t)$

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

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

$4 t^{4} - 1 \cdot 8 (t^{2} t^{1})$

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

$4 t^{4} - 1 \cdot 8 t^{2 + 1}$

Add $2$ and $1$ .

$4 t^{4} - 1 \cdot 8 t^{3}$

Multiply $- 1$ by $8$ .

$4 t^{4} - 8 t^{3}$