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 $(a + b)^2$

The formula is $(a + b)^2=a^{2}+2ab + b^{2}$. In the expression $(-2m + 5n)^2$, $a=-2m$ 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

$(-2m + 5n)^2=a^{2}+2ab + b^{2}=4m^{2}-20mn + 25n^{2}$. And $(a + b)^2$ is a perfect - square trinomial.

Answer:

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