Algebraic Expressions and Substitution

Terms, coefficients, collecting like terms, expanding single brackets, and numerical substitution.

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Curated Video Lesson

Visual explanation and practical step-by-step walk-through

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Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

Algebra is the branch of mathematics where letters and symbols represent unknown quantities and relationships. In JHS 1, students transition from plain numerical arithmetic to symbolic reasoning. Algebraic skills are essential for science, economics, computer programming, and everyday problem-solving. In the BECE exam, questions on simplifying expressions, collecting like terms, expanding brackets, and substitution appear every single year.

What You Will Master in This Lesson (NaCCA Objectives):

Define algebraic terms, variables, coefficients, and constants.

Identify like terms and unlike terms in algebraic expressions.

Simplify algebraic expressions by grouping and collecting like terms.

Apply the distributive law to expand single brackets.

Substitute positive and negative numbers into algebraic expressions and evaluate correctly.

1. Anatomy of an Algebraic Term

In the term 7x²: • 7 is the Coefficient (numerical factor). • x is the Variable (the unknown letter). • 2 is the Power / Index (exponent). In 4x - 9, -9 is a Constant term (fixed number with no variable).

2. Like Terms vs Unlike Terms

• Like Terms: Terms that have the exact same variables raised to the exact same powers (e.g. 3x and 5x, 7ab and -2ab). ONLY like terms can be added or subtracted! • Unlike Terms: Terms with different variables or powers (e.g. 3x and 3y, 5a and 5a²). Unlike terms CANNOT be merged! (3x + 2y does NOT equal 5xy).

3. Expanding Single Brackets (Distributive Law)

Formula: a(b + c) = ab + ac and a(b - c) = ab - ac. Watch signs when outside term is negative: Formula: -a(b - c) = -ab + ac (negative × negative = positive). Example: -3(4x - 5) = -12x + 15.

4. Substitution and Evaluation

Replace letters with specific numbers and calculate using standard arithmetic. Golden Rule for Negative Values: Always place negative numbers in brackets! If x = -3: • 2x = 2(-3) = -6 • x² = (-3)² = +9 • -x² = -((-3)²) = -9

Common Mistakes Students Make in BECE Examinations:

⚠️Combining unlike terms: Writing 5x + 3y = 8xy.

⚠️Sign errors during expansion: Writing -(x - 4) as -x - 4 instead of -x + 4.

⚠️Squaring negative numbers without brackets: Writing -3² = 9 instead of (-3)² = 9.

Teacher's BECE Exam Pro-Tips:

⭐Underline like terms with their preceding signs before grouping.

⭐Always expand brackets first before attempting to collect like terms.

⭐Put negative substituted numbers in parentheses.

Quick Revision Summary Checklist:

Coefficient: the number before a letter.

Only like terms can be combined.

Distributive Law: a(b + c) = ab + ac.

Negative outside bracket flips all signs inside.

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Collecting Like Terms

Problem StatementSimplify: 5x + 3y - 2x + 7y

Step-by-Step Solution:

Step 1: Group like terms: (5x - 2x) + (3y + 7y).

Step 2: Combine coefficients: 3x + 10y.

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Key Takeaway / Exam Rule: Never combine unlike terms: 3x + 10y cannot be written as 13xy!

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