michelleclark
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Which is equivalent to (−2m + 5n)2, and what type of special product is it4m2 + 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

Respuesta :

arthurpdc
We'll calculate the product:

[tex](-2m+5n)^2=(-2m+5n)(-2m+5n)\\\\ (-2m+5n)^2=(-2m)\cdot(-2m+5n)+(5n)(-2m+5n)\\\\ (-2m+5n)^2=[(-2m)\cdot(-2m)+(-2m)\cdot(5n)]+[(5n)\cdot(-2m)+(5n)\cdot(5n)]\\\\ (-2m+5n)^2=4m^2-10mn-10mn+25n^2\\\\ (-2m+5n)^2=4m^2-20mn+25n^2[/tex]

So, the answer is:

[tex]4m^2-20mn+25n^2,~\text{a perferct square trinomial.}[/tex]

The concept of the square is applied that is the multiplication of the term itself two times.

The equivalent function of [tex]\rm (-2m + 5n)^2[/tex] is [tex]\rm 4m^2 - 20mn + 25n^2[/tex].

What is an equivalent function?

The equivalent is the functions that are in different forms but are equal to the same value.

Given

(-2m + 5n)² is a function.

To find

The equivalent function of (-2m + 5n)².

We know that this can be written as

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

On multiply, we have

[tex]\rm (-2m + 5n)(-2m + 5n)\\\\-2m(-2m + 5n) + 5n(-2m + 5n)\\\\(-2m)^2 - 10mn -10mn + (5n)^2\\\\4m^2 - 20mn + 25n^2[/tex]

Thus, the equivalent function of (-2m + 5n)² is 4m² - 20mn + 25n².

More about the equivalent function link is given below.

https://brainly.com/question/10498970

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