Simplify (1-2m^3+2m^4)-(5m^3+7-7m^4)

$(1 - 2 m^{3} + 2 m^{4}) - (5 m^{3} + 7 - 7 m^{4})$

Step 1

Simplify each term.

Apply the distributive property.

$1 - 2 m^{3} + 2 m^{4} - (5 m^{3}) - 1 \cdot 7 - (- 7 m^{4})$

Simplify.

Multiply $5$ by $- 1$ .

$1 - 2 m^{3} + 2 m^{4} - 5 m^{3} - 1 \cdot 7 - (- 7 m^{4})$

Multiply $- 1$ by $7$ .

$1 - 2 m^{3} + 2 m^{4} - 5 m^{3} - 7 - (- 7 m^{4})$

Multiply $- 7$ by $- 1$ .

$1 - 2 m^{3} + 2 m^{4} - 5 m^{3} - 7 + 7 m^{4}$

Step 2

Simplify by adding terms.

Subtract $7$ from $1$ .

$- 2 m^{3} + 2 m^{4} - 5 m^{3} - 6 + 7 m^{4}$

Subtract $5 m^{3}$ from $- 2 m^{3}$ .

$2 m^{4} - 7 m^{3} - 6 + 7 m^{4}$

Add $2 m^{4}$ and $7 m^{4}$ .

$9 m^{4} - 7 m^{3} - 6$