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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

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CoastsideDad

Answer:

4 m squared minus 20 m n + 25 n squared; a perfect square trinomial

Step-by-step explanation:

(-2m+5n)(-2m+5n)

4[tex]m^{2}[/tex]-20mn+25[tex]n^{2}[/tex]

facundo3141592

By expanding the given expression, we conclude that the equivalent expression will be the perfect square trinomial:

4m^2 + 20m*n + 25n^2

How to get an equivalent expression to the given binomial?

We have a polynomial given by the expression:

(2m + 5n)^2

If we expand the binomial (binomial means that it hastwo terms), we will get:

(2m)^2 + 2*(2m)*(5n) + (5n)^2

= 4m^2 + 20m*n + 25n^2

This is a perfect square trinomial (trinomial because has 3 terms and perfect square because is the square of a binomial).

If you want to learn more about polynomials, you can read:

https://brainly.com/question/4142886

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