What should be added to the (a-b)^2 to make it equal to a^2-b^2

Question

asked May 10, 2024 75.3k views

1 Answer

Hossein Golshani · Answer 1 · 2024-05-16T01:47:24+0000

To make ^2 equal to a^2-b^2, you must add -2ab-2b^2

The question requires us to find what should be added to (a-b)^2 to make it equal to a^2-b^2. By expanding (a-b)^2, we get a^2 - 2ab + b^2.

To transform this expression into a^2 - b^2, we must subtract the extra term 2ab and also subtract b^2 which is present instead of -b^2.

Therefore, we must add -2ab, and an additional -2b^2 (which is equivalent to subtracting 2b^2) to (a-b)^2 to make it equal to a^2 - b^2.