(2m^2-5n^2)^2

Jasonbradley

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Jun 16, 2024

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Expanding (2m^2 - 5n^2)^2

The expression (2m^2 - 5n^2)^2 represents the square of a binomial. To expand it, we can use the following formula:

(a - b)^2 = a^2 - 2ab + b^2

Here's how we apply it:

1. Identify 'a' and 'b':

   • In our case, a = 2m^2 and b = 5n^2

2. Substitute into the formula:

   • (2m^2 - 5n^2)^2 = (2m^2)^2 - 2(2m^2)(5n^2) + (5n^2)^2

3. Simplify:

   • (2m^2)^2 = 4m^4
   • 2(2m^2)(5n^2) = 20m^2n^2
   • (5n^2)^2 = 25n^4

4. Combine the terms:

   • (2m^2 - 5n^2)^2 = 4m^4 - 20m^2n^2 + 25n^4

Therefore, the expanded form of (2m^2 - 5n^2)^2 is 4m^4 - 20m^2n^2 + 25n^4.