Binomial Expressions — O/L Mathematics

What must I remember about Binomial Expressions?

• Expansion of square of a sum: (a + b)² = a² + 2ab + b² (first term squared + twice product + second term squared).
• Expansion of square of a difference: (a - b)² = a² - 2ab + b² (middle term carries a negative sign).
• Product of two binomials with common linear term: (x + a)(x + b) = x² + (a + b)x + ab.
• Difference of two squares expansion: (a + b)(a - b) = a² - b² (the linear cross-terms cancel out completely).
• Geometric models: Representing binomial expansions visually using areas of subdivided rectangles and squares.

Test yourself (1 minute)

1. The dropped middle term trap

   Writing (a + b)² = a² + b² or (a - b)² = a² - b² is a severe algebraic blunder; never omit the middle term ±2ab.

2. Sign rule for (a - b)²

   The final term +b² is ALWAYS positive because (-b)² = +b²; only the middle term -2ab is negative.

3. Mental arithmetic evaluation

   Use algebraic identities for rapid numerical calculations, such as 102² = (100 + 2)² = 10000 + 400 + 4 = 10404.

Practise Binomial Expressions questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 4)

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Where does Binomial Expressions fit in the syllabus?

Grade 10 · Term 1 · Grade 11 · Term 1