Simplify 2z^2(m^3-4m^8)-8m^5+m^10

$2 z^{2} (m^{3} - 4 m^{8}) - 8 m^{5} + m^{10}$

Step 1

Simplify each term.

Apply the distributive property.

$2 z^{2} m^{3} + 2 z^{2} (- 4 m^{8}) - 8 m^{5} + m^{10}$

Rewrite using the commutative property of multiplication.

$2 z^{2} m^{3} + 2 \cdot - 4 z^{2} m^{8} - 8 m^{5} + m^{10}$

Multiply $2$ by $- 4$ .

$2 z^{2} m^{3} - 8 z^{2} m^{8} - 8 m^{5} + m^{10}$

Step 2

Reorder.

Move $z^{2}$ .

$2 m^{3} z^{2} - 8 z^{2} m^{8} - 8 m^{5} + m^{10}$

Move $z^{2}$ .

$2 m^{3} z^{2} - 8 m^{8} z^{2} - 8 m^{5} + m^{10}$

Move $- 8 m^{5}$ .

$2 m^{3} z^{2} - 8 m^{8} z^{2} + m^{10} - 8 m^{5}$

Move $2 m^{3} z^{2}$ .

$- 8 m^{8} z^{2} + m^{10} + 2 m^{3} z^{2} - 8 m^{5}$