- A
- B
- C
- D
Step-by-Step Solution
Commutativity rewrites the first product as , so is a common factor. Then . The trap is losing the negative sign while factoring, since only the bracket is left positive.
Answer: B)
Use the properties (not brute force) to compute .
Class 8Rational NumbersRational Numbers
Key idea: Properties at a glance
| Property | Addition | Subtraction | Multiplication | Division |
|---|---|---|---|---|
| Closure | ✓ | ✓ | ✓ | ✓ (b ≠ 0) |
| Commutative | ✓ | ✗ | ✓ | ✗ |
| Associative | ✓ | ✗ | ✓ | ✗ |
Distributive: multiplication distributes over addition AND subtraction. a × (b + c) = ab + ac, and a × (b − c) = ab − ac.
|---|---|---|---|---|
| Closure | ✓ | ✓ | ✓ | ✓ (b ≠ 0) |
| Commutative | ✓ | ✗ | ✓ | ✗ |
| Associative | ✓ | ✗ | ✓ | ✗ |
Distributive: multiplication distributes over addition AND subtraction. a × (b + c) = ab + ac, and a × (b − c) = ab − ac.
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