Simplify:
​$$(x^2+m^2-z^2 )^2-(x^2-m^2+z^2 )^2=$$​​

Correct option is B

Given:

​$$(x^2+m^2-z^2 )^2-(x^2-m^2+z^2 )^2$$

Formula used:

​$$A^2−B^2=(A+B)(A−B).$$

Solution:

​$$A=x ^2 +m ^2 −z ^2 ,B=x ^2 −m ^2 +z ^2$$

​​So, the expression becomes:

​$$(x ^2 +m ^2 −z ^2 ) ^2 −(x ^2 −m ^2 +z ^2 ) ^2 =(A+B)(A−B)$$

Calculating A+B ;

​$$A+B=(x ^2 +m ^2 −z ^2 )+(x ^2 −m ^2 +z ^2 )$$

​​$$A+B=x ^2 +x ^2 +m ^2 −m ^2 −z ^2 +z ^2$$

​​$$A+B=2x ^2$$

Calculating A- B

​$$A−B=(x ^2 +m ^2 −z ^2 )−(x ^2 −m ^2 +z ^2 )$$

​​$$A−B=x ^2 +m ^2 −z ^2 −x ^2 +m ^2 −z ^2$$

​​$$A−B=m ^2 +m ^2 −z ^2 −z ^2$$

​​$$A−B=2m ^2 −2z ^2$$

Now, 

​$$(A+B)(A−B)=(2x ^2 )(2m ^2 −2z ^2 )$$

​​$$(A+B)(A−B)=4x ^2 (m ^2 −z ^2 )$$

So, the simplified form of the given expression is:

= $$4x ^2 (m ^2 −z ^2 )$$​​

Thus, correct option is (b)