Solve 86(m+n)(m-n)+3n(m-n)

$$86 ( m + n ) ( m - n ) + 3 n ( m - n )$$

Evaluate

$$\left(m-n\right)\left(86m+89n\right)$$

Solution Steps

Use the distributive property to multiply 86 by m+n.

$$\left(86m+86n\right)\left(m-n\right)+3n\left(m-n\right)$$

Apply the distributive property by multiplying each term of 86m+86n by each term of m-n.

$$86m^{2}-86mn+86nm-86n^{2}+3n\left(m-n\right)$$

Combine -86mn and 86nm to get 0.

$$86m^{2}-86n^{2}+3n\left(m-n\right)$$

Use the distributive property to multiply 3n by m-n.

$$86m^{2}-86n^{2}+3nm-3n^{2}$$

Combine -86n^{2} and -3n^{2} to get -89n^{2}.

$$86m^{2}-89n^{2}+3nm$$

Expand

$$86m^{2}+3mn-89n^{2}$$

Solution Steps

Use the distributive property to multiply 86 by m+n.

$$\left(86m+86n\right)\left(m-n\right)+3n\left(m-n\right)$$

Apply the distributive property by multiplying each term of 86m+86n by each term of m-n.

$$86m^{2}-86mn+86nm-86n^{2}+3n\left(m-n\right)$$

Combine -86mn and 86nm to get 0.

$$86m^{2}-86n^{2}+3n\left(m-n\right)$$

Use the distributive property to multiply 3n by m-n.

$$86m^{2}-86n^{2}+3nm-3n^{2}$$

Combine -86n^{2} and -3n^{2} to get -89n^{2}.

$$86m^{2}-89n^{2}+3nm$$