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

$$( 2 m + n - p ) \quad ( 2 m - n + p$$

Evaluate

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

Solution Steps

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

$$4m^{2}-2mn+2mp+2nm-n^{2}+np-2pm+pn-p^{2}$$

Combine -2mn and 2nm to get 0.

$$4m^{2}+2mp-n^{2}+np-2pm+pn-p^{2}$$

Combine 2mp and -2pm to get 0.

$$4m^{2}-n^{2}+np+pn-p^{2}$$

Combine np and pn to get 2np.

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

Expand

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

Solution Steps

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

$$4m^{2}-2mn+2mp+2nm-n^{2}+np-2pm+pn-p^{2}$$

Combine -2mn and 2nm to get 0.

$$4m^{2}+2mp-n^{2}+np-2pm+pn-p^{2}$$

Combine 2mp and -2pm to get 0.

$$4m^{2}-n^{2}+np+pn-p^{2}$$

Combine np and pn to get 2np.

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