Meson African Motives: Mathematics Grade N - Algebraic Expressions Revision

Introduction

• Focus on typical exam questions for revision.
• Topics covered: Simplification, factorization of algebraic expressions.

Question 3.1: Simplifying Expressions

Simplifying by Adding/Subtracting Like Terms (3.1.1)

• Given Expression: (-4x + 6 + 11x - 5)
• Process:
  • Combine like terms (terms with 'x' and constants separately).
  • (-4x + 11x = 7x)
  • (6 - 5 = 1)
• Result: Simplified expression is (7x + 1).

Simplifying by Multiplying Brackets (3.1.2)

• Given Expression: Multiply three by bracket ((x - 1)) and (-4) by bracket ((x + 2)).
• Process:
  • Expand using distributive property: (3(x - 1) = 3x - 3) and (-4(x + 2) = -4x - 8).
  • Combine like terms: (3x - 4x = -x); (-3 + 8 = 5).
• Result: Simplified expression is (-x + 5).

Substituting Values (3.1.3)

• Expression: (2x^2 - 4) with (x = 3).
• Process:
  • Substitute (x = 3) into the expression.
  • Calculate: (2(3)^2 - 4 = 18 - 4 = 14).
• Result: The value is (14).

Question 3.2: Laws of Exponents

Simplifying Exponents (3.2.1)

• Given Expression: (\frac{5x^3 y \cdot (2xy^2)^2}{15x^5 y^2})
• Process:
  • Expand ((2xy^2)^2 = 4x^2y^4).
  • Combine with (5x^3y): (20x^5y^5).
  • Simplify: Divide by (15x^5y^2).
  • Cancel common terms to get (\frac{20}{15} = \frac{4}{3}) and (y^3).
• Result: Simplified expression is (\frac{4y^3}{3}).

Simplifying Fractions (3.2.2)

• Given Expression: (\frac{2x + 4y}{x + 2y})
• Process:
  • Factor out common factors in numerator: (2(x + 2y)).
  • Cancel out (x + 2y) in numerator and denominator.
• Result: Simplified expression is (2).

Question 3.3: Factorization Techniques

Factorizing Quadratics (3.3.1)

• Expression: (x^2 - x - 6)
• Process:
  • Use the product-sum method to factor: Factors of (-6) that sum to (-1) are (-3) and (2).
  • Factorized form: ((x - 3)(x + 2)).

Factorizing Binomials (3.3.2)

• Expression: (18x^2 - 200)
• Process:
  • Find the highest common factor (HCF), which is (2).
  • Factor out (2): get (2(9x^2 - 100)).
  • Recognize as a difference of squares: (9x^2 - 100 = (3x - 10)(3x + 10)).
• Result: Final factorized form: (2(3x - 10)(3x + 10)).

Conclusion

• Understanding algebraic expressions involves recognizing patterns, applying laws of exponents, and proper factorization techniques.
• Practice these methods to achieve full marks in exams.