Assertion : In `10xy, -7y, -8x, x^(2)y^(2), 100y^(2), -12x^(2)y^(2), 5x^(2), 3y` like terms are `-7y" and "3y, x^(2)y^(2)" and "-12x^(2)y^(2)`.
Reason : Terms which have the same algebraic factors are like terms.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Identify the terms in the expression
The given expression is:
\[ 10xy, -7y, -8x, x^2y^2, 100y^2, -12x^2y^2, 5x^2, 3y \]

### Step 2: Group the terms based on their variables
We will group the terms based on their algebraic factors (variables):
- Terms with **y**: \(-7y\), \(3y\)
- Terms with **x²y²**: \(x^2y^2\), \(-12x^2y^2\)
- Other terms: \(10xy\), \(-8x\), \(100y^2\), \(5x^2\)

### Step 3: Identify like terms
Like terms are those that have the same variables raised to the same powers:
- The like terms in the group of **y** are \(-7y\) and \(3y\).
- The like terms in the group of **x²y²** are \(x^2y^2\) and \(-12x^2y^2\).

### Step 4: Confirm the assertion
The assertion states that the like terms are \(-7y\) and \(3y\), and \(x^2y^2\) and \(-12x^2y^2\). We have confirmed that these pairs are indeed like terms.

### Step 5: Confirm the reason
The reason states that terms which have the same algebraic factors are like terms. This is correct as we have identified that the pairs of terms share the same variables raised to the same powers.

### Conclusion
Both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer
The assertion is correct, and the reason is also correct. The reason is the correct explanation for the assertion.

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