WAEC 2022 Mathematics · Question 19
Simplify
Options
- A.2[1+3m]
- B.2[1-3m]
- C.2[1-3m]
- D.2[1+3m]
Answer: B. 2[1-3m]
Explanation written with AI and checked against the answer key
Analyze the question: We need to simplify a fraction whose numerator is 2 − 18m². The key is to factorise the numerator and cancel the common factor with the denominator. Concept: Difference of two squares: a² − b² = (a − b)(a + b) Solution: Step 1: Take out the common factor 2 from the numerator: 2 − 18m² = 2(1 − 9m²) Step 2: Recognise 1 − 9m² as a difference of two squares, since 9m² = (3m)²: 1 − 9m² = (1 − 3m)(1 + 3m) Step 3: Substitute back into the fraction: (2 − 18m²)/(1 + 3m) = 2(1 − 3m)(1 + 3m)/(1 + 3m) Step 4: Cancel (1 + 3m) from the top and bottom (for m ≠ −1/3): = 2(1 − 3m) Checking with a value: Let m = 1. The original expression gives (2 − 18)/(1 + 3) = −16/4 = −4. Option B gives 2(1 − 3) = −4. ✓ Answer: Option B, 2[1 − 3m]. Tip: When you see a numerator like a − b·m² with a denominator of the form (x + y·m), first take out any common number, then check for a difference of two squares. The factor in the denominator often cancels. Always test with a simple number like m = 1 to confirm quickly in the exam.AI can make mistakes. Report anything that looks wrong.
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