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Which is equivalent to (−2m + 5n)2, and what type of special product is it? 4m2 + 25n2; a perfect square trinomial 4m2 + 25n2; the difference of squares 4m2 − 20mn + 25n2; a perfect square trinomial 4m2 − 20mn + 25n2; the difference of squares

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sqdancefan
(-2m +5n)^2 is a perfect square.
It expands to the trinomial 4m^2 -20mn +25n^2, a "perfect square trinomial."

A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]

What is expression?

"It is a mathematical statement which consists of numbers, variables and some mathematical operations."

What is trinomial?

"It is a polynomial which has only three terms."

What is perfect square trinomial?

"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."

For given question,

We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].

We need to find to find an equivalent expression to given expression.

Consider given expression,

[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]

We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.

Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]

Learn more about perfect square trinomial here:

https://brainly.com/question/16615974

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