Question

Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it?

4 m squared + 25 n squared; a perfect square trinomial
4 m squared + 25 n squared; the difference of squares
4 m squared minus 20 m n + 25 n squared; a perfect square trinomial
4 m squared minus 20 m n + 25 n squared; the difference of squares

Answer 1

4m^2 − 20mn + 25n^2; a perfect square trinomial.

Explanation: (-2m + 5n)^2 = (-2m)^2 + 2(-2m)(5n) + (5n)^2 = 4m^2 − 20mn + 25n^2, which is a perfect square trinomial.