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

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

Evaluate

$$-m\left(m+2n\right)$$

Solution Steps

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

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

Multiply -2 and -1 to get 2.

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

Multiply -1 and -1 to get 1.

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

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

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

Combine 2mn and -2nm to get 0.

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

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

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

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

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

Combine -4mn and 2nm to get -2mn.

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

Combine m^{2} and -2m^{2} to get -m^{2}.

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

Combine -4n^{2} and 4n^{2} to get 0.

$$-m^{2}-2mn$$

Expand

$$-m^{2}-2mn$$

Solution Steps

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

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

Multiply -2 and -1 to get 2.

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

Multiply -1 and -1 to get 1.

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

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

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

Combine 2mn and -2nm to get 0.

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

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

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

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

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

Combine -4mn and 2nm to get -2mn.

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

Combine m^{2} and -2m^{2} to get -m^{2}.

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

Combine -4n^{2} and 4n^{2} to get 0.

$$-m^{2}-2mn$$