HSSC CET · Bite-size lessons

Algebra

About 6 min · Quantitative Ability · English

Time worked out from the lesson's 390 words at 150 words a minute, plus a minute for each question.

Algebra forms the foundation of quantitative reasoning in competitive exams. For HSSC CET, you need to master algebraic expressions, standard identities, and solving linear equations. These concepts appear directly as standalone questions and indirectly when solving problems on percentages, profit-loss, time-work, and other arithmetic topics.

Key ideas

• Algebraic Expression: A combination of constants, variables, and operations (e.g., 3x² + 5x − 7). Terms are separated by + or − signs.
• Polynomial Degree: The highest power of the variable. In 4x³ + 2x − 1, the degree is 3.
• Like Terms: Terms with identical variable parts (e.g., 3xy and −5xy). Only like terms can be added or subtracted directly.
• Identity vs Equation: An identity holds true for all values of variables (e.g., (a + b)² = a² + 2ab + b²). An equation is true only for specific values.
• Linear Equation in One Variable: Form ax + b = 0. Solution: x = −b/a.

Watch out for

• Forgetting the middle term in squares: Students write (a + b)² = a² + b², missing 2ab. → Always remember: square of sum = sum of squares + twice the product.
• Sign errors in (a − b)²: Writing (a − b)² = a² + 2ab + b² instead of a² − 2ab + b². → The middle term takes the sign from the bracket.
• Confusing a³ + b³ with (a + b)³: These are different expressions. a³ + b³ = (a + b)(a² − ab + b²), not (a + b)³. → Check by substituting a = 1, b = 1 to verify your formula.

Quick reference

• (a + b)² = a² + 2ab + b² — never forget the middle term
• a² − b² = (a + b)(a − b) — difference of squares always factors
• If x + 1/x = k, then x² + 1/x² = k² − 2
• If a + b + c = 0, then a³ + b³ + c³ = 3abc
• Unique solution: a₁/a₂ ≠ b₁/b₂ — ratios must be unequal

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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