%5E2.jpeg "(2m^2-5n^2)^2")
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:
-
Identify 'a' and 'b':
- In our case, a = 2m^2 and b = 5n^2
-
Substitute into the formula:
- (2m^2 - 5n^2)^2 = (2m^2)^2 - 2(2m^2)(5n^2) + (5n^2)^2
-
Simplify:
- (2m^2)^2 = 4m^4
- 2(2m^2)(5n^2) = 20m^2n^2
- (5n^2)^2 = 25n^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.