which is equivalent to (-2m + 5n)^2, and what type of special product is it?\n4m^2+25n^2; a perfect square…

Explanation:

Step1: Recall the formula for ((a + b)^2)

((a + b)^2=a^{2}+2ab + b^{2}). Here (a=-2m) and (b = 5n).

Step2: Calculate (a^{2})

(a^{2}=(-2m)^{2}=(-2)^{2}\times m^{2}=4m^{2})

Step3: Calculate (2ab)

(2ab=2\times(-2m)\times5n=-20mn)

Step4: Calculate (b^{2})

(b^{2}=(5n)^{2}=25n^{2})

Step5: Combine the terms

((-2m + 5n)^{2}=4m^{2}-20mn + 25n^{2}), and it is a perfect - square trinomial since it is in the form of ((a + b)^2=a^{2}+2ab + b^{2}).

Answer:

C. (4m^{2}-20mn + 25n^{2}); a perfect square trinomial