Question

(a+2)^2= (x-3)^2= a^2+4ab+4b^2= 9m^2-6mn+n^2= 25a^2-9b^2=

Answer 1

$(a+2)^2=a^2+4a+4\\\\(x-3)^2=x^2-6x+9\\\\a^2+4ab+4b^2=(a+2b)^2\\\\9m^2-6mn+n^2=(3m-n)^2\\\\25a^2-9b^2=(5a-3b)(5a+3b)$

Answer 2

To solve each of these equations, let's take them one by one:

1. (a+2)^2 = a^2 + 4ab + 4b^2

In this equation, we have an expression in terms of (a+2)^2 and another expression in terms of a^2 + 4ab + 4b^2. Since these two expressions are equal, their corresponding terms must be equal.

a^2 + 4ab + 4b^2 = a^2 + 4ab + 4b^2

This equation holds true for any values of 'a' and 'b', as the left-hand side and right-hand side are the same.

2. (x-3)^2 = 9m^2 - 6mn + n^2

Similar to the previous equation, we have two expressions that are equal. So we equate their corresponding terms.

x^2 - 6x + 9 = 9m^2 - 6mn + n^2

This equation holds true for any values of 'x', 'm', and 'n' as the left-hand side and right-hand side are the same.

3. 25a^2 - 9b^2 = a^2 + 4ab + 4b^2

Again, we equate corresponding terms.

25a^2 - 9b^2 = a^2 + 4ab + 4b^2

Now, we need to solve this equation for 'a' and 'b'. Let's move all terms to one side:

25a^2 - 9b^2 - a^2 - 4ab - 4b^2 = 0

Combine like terms:

24a^2 - 4ab - 13b^2 = 0

Unfortunately, this is not a simple equation to solve, as it is a quadratic equation with two variables. We cannot find a unique solution for 'a' and 'b' without additional information or constraints.

If you have more information or specific constraints related to 'a' and 'b', please provide them, and I can try to help you further with the solution. Otherwise, this equation has multiple solutions depending on the values of 'a' and 'b'.