If 𝑎𝑏 = 𝑘[(𝑎 + 𝑏)2 − (𝑎 − 𝑏)2] , find 𝑘 =？

To find the value of k, we need to simplify the right side of the equation and then isolate k. Here are the steps:

1. Expand the squares in the brackets: (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2

2. Substitute these expansions into the equation: k[(a + b)^2 - (a - b)^2] = k[(a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)]

3. Simplify the equation inside the brackets: = k[4ab]

4. Now, we know that ab = k[4ab]. To isolate k, we divide both sides of the equation by 4ab: k = ab / 4ab

5. Simplify the equation to find the value of k: k = 1/4

So, the value of k is 1/4.