Solve (2m^2n+1)(-2m^2n+1)+4(m^4n^2+1)

$$( 2 m ^ { 2 } n + 1 ) ( - 2 m ^ { 2 } n + 1 ) + 4 ( m ^ { 4 } n ^ { 2 } + 1 )$$

Evaluate

$$5$$

Solution Steps

Use the distributive property to multiply 2m^{2}n+1 by -2m^{2}n+1 and combine like terms.

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

Use the distributive property to multiply 4 by m^{4}n^{2}+1.

$$-4m^{4}n^{2}+1+4m^{4}n^{2}+4$$

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

$$1+4$$

Add 1 and 4 to get 5.

$$5$$

Factor

$$5$$