CORE_MATH • SHS 1Term 1WAEC / WASSCE SyllabusVIP Lesson
Algebraic Expressions, Expansion & Factorization
Expanding binomials and trinomials, factorization by grouping, difference of two squares, and quadratic trinomial factorization.
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Real-World Context & Relevance in Ghana
Quantity surveyors in Accra estimating paving blocks use algebraic expressions to express total border area and tile requirements as a function of room dimensions.
Key Syllabus Learning Objectives
- 1Expand products of binomials and trinomials systematically
- 2Factorize four-term algebraic expressions by grouping terms
- 3Recognize and factor difference of two squares and perfect squares
- 4Factorize quadratic expressions ax² + bx + c where a ≠ 1
1
Factoring Quadratic Trinomials ax² + bx + c
To factorize when a ≠ 1: multiply a and c to find the product ac. Identify two integers p and q whose product is ac and whose sum is b. Split the middle term bx into px + qx, then factorize by grouping.
- Compute product = a × c and sum = b.
- List factor pairs of ac and find the pair summing to b.
- Replace bx with the two terms.
- Factor by grouping the first two and last two terms.
Core Takeaway:
Never guess factors; use the product-sum method methodically.
WAEC / WASSCE Examiner Tips
- Watch negative signs carefully when expanding (a - b)². The middle term is always -2ab, but the last term is +b².
- In difference of two squares questions, check if terms can be factored further (e.g. x⁴ - y⁴ = (x² + y²)(x + y)(x - y)).
- WAEC awards M1 for correctly splitting the middle term.
Common Candidate Pitfalls & Errors to Avoid
- Writing (a + b)² = a² + b² (omitting the 2ab middle term).
- Missing negative sign distribution when factoring by grouping: e.g. -2(x - 3) = -2x + 6.
- Leaving common numerical factors unfactored in the final expression.
Topic Mastery Checklist
- Can I expand (2x - 5)(3x + 4)?
- Can I factorize 4a² - 25b²?
- Can I factorize 6x² - 11x - 10?
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