Solve (-m+2n)(-2n-m)-2(m-1

$$( - m + 2 n ) ( - 2 n - m ) - 2 ( m - 1$$

Evaluate

$$m^{2}-2m-4n^{2}+2$$

Solution Steps

Apply the distributive property by multiplying each term of -m+2n by each term of -2n-m.

$$-2\left(-m\right)n-\left(-m\right)m-4n^{2}-2nm-2\left(m-1\right)$$

Multiply -2 and -1 to get 2.

$$2mn-\left(-m\right)m-4n^{2}-2nm-2\left(m-1\right)$$

Multiply -1 and -1 to get 1.

$$2mn+mm-4n^{2}-2nm-2\left(m-1\right)$$

Multiply m and m to get m^{2}.

$$2mn+m^{2}-4n^{2}-2nm-2\left(m-1\right)$$

Combine 2mn and -2nm to get 0.

$$m^{2}-4n^{2}-2\left(m-1\right)$$

Use the distributive property to multiply -2 by m-1.

$$m^{2}-4n^{2}-2m+2$$

Expand

$$m^{2}-2m-4n^{2}+2$$

Solution Steps

Apply the distributive property by multiplying each term of -m+2n by each term of -2n-m.

$$-2\left(-m\right)n-\left(-m\right)m-4n^{2}-2nm-2\left(m-1\right)$$

Multiply -2 and -1 to get 2.

$$2mn-\left(-m\right)m-4n^{2}-2nm-2\left(m-1\right)$$

Multiply -1 and -1 to get 1.

$$2mn+mm-4n^{2}-2nm-2\left(m-1\right)$$

Multiply m and m to get m^{2}.

$$2mn+m^{2}-4n^{2}-2nm-2\left(m-1\right)$$

Combine 2mn and -2nm to get 0.

$$m^{2}-4n^{2}-2\left(m-1\right)$$

Use the distributive property to multiply -2 by m-1.

$$m^{2}-4n^{2}-2m+2$$