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

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

Expand

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

Solution Steps

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

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

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

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

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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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