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Identify the polynomial that is the difference of two squares.

25m^2 − 16n
9m^2 − 5n^6
49m^2 − 81n^4
36m^2 − 8n^8

User Trent Gm
by
7.7k points

1 Answer

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Answer:


25m² − 16n

Explanation:

The polynomial that is the difference of two squares is:


25m^2 − 16n

To see why, we can try to factor each polynomial. For example:


9m^2 − 5n^6 = (3m)^2 − (n^3)^2


49m^2 − 81n^4 = (7m)^2 − (9n^2)^2


36m^2 − 8n^8 = (6m)^2 − (2n^4)^2

Notice that for each of these polynomials, we can factor them into the difference of two squares. However, for the polynomial 25m² − 16n, we can directly see that it is the difference of two squares because:


25m^2 − 16n = (5m)^2 − (4n)^2

Therefore, 25m² − 16n is the polynomial that is the difference of two squares.

User Dan Jameson
by
8.1k points
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