Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Equivalent expressions |
Grade: 1400-a Lesson: S1-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
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 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 |
Step |
So, the simplified form of the expression is 2b. |
|
6 |
Choice.A |
This choice is wrong as it’s a fixed term, unrelated to variables a or b, lacking simplification |
-2ab |
7 |
Choice.B |
2a is not the simplified expression; it simplifies to 2b, suggesting option B’s inaccuracy |
2a |
8 |
Choice.C |
Option C incorrectly suggests multiplication, but the expression involves the difference of square roots |
4ab |
9 |
Choice.D |
This option is correct because it correctly represents the simplified expression |
2b |
10 |
Answer |
Option |
D |
11 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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