1

Problem

Simplify the expression: \$\sqrt(a^2 + 2ab + b^2) - \sqrt(a^2 - 2ab + b^2)\$.

2

Step

The given expression is

\$\sqrt(a^2 + 2ab + b^2) - \sqrt(a^2 - 2ab + b^2)\$

3

Formula

The factorization formula are:
\$ (a+b)^2 = a^2 + 2ab + b^2 \$

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

4

Step

Now plug the condition from above equation:

\$ \sqrt ((a+b)^2) - \sqrt((a-b)^2) \$

a + b - ( a - b )

a + b - a + b

2b

5

Solution

So, the simplified form of the expression is 2b.

6

Sumup

Please summarize steps

Choices

7

Choice-A

This choice is wrong as it’s a fixed term, unrelated to variables a or b, lacking simplification

Wrong - 2ab

8

Choice-B

2a is not the simplified expression; it simplifies to 2b, suggesting option B’s inaccuracy

Wrong 2a

9

Choice-C

Option C incorrectly suggests multiplication, but the expression involves the difference of square roots

Wrong 4ab

10

Choice-D

This option is correct because it correctly represents the simplified expression

Correct 2b

11

Answer

Option

D

12

Sumup

Please summarize choices