DepEd MELC reviewer for Grade 8 Mathematics, Quarter 1. Study the rules, worked formulas, and exam hacks below.
1
Special Products
(a+b)² = a² + 2ab + b²
(a−b)² = a² − 2ab + b²
(a+b)(a−b) = a² − b²
(a−b)² = a² − 2ab + b²
(a+b)(a−b) = a² − b²
💡 Exam Hack
Memorize these patterns — they let you expand and factor instantly without long multiplication.
2
Factoring Techniques
| Type | Pattern |
|---|---|
| Common monomial | ax + ay = a(x+y) |
| Difference of squares | a²−b² = (a+b)(a−b) |
| Perfect square trinomial | a²±2ab+b² = (a±b)² |
| General trinomial | x²+5x+6 = (x+2)(x+3) |
3
Rational Algebraic Expressions
A rational expression is a fraction with polynomials. Simplify by factoring and cancelling common factors.
⚠️ Common Mistake
Only cancel FACTORS, never individual terms. In (x+2)/(x+3) you cannot cancel the x.
4
Worked Example
Factor x² − 9 and x² + 7x + 12.
x² − 9 = (x+3)(x−3)
x² + 7x + 12 = (x+3)(x+4)
x² + 7x + 12 = (x+3)(x+4)
For the trinomial, find two numbers that multiply to 12 and add to 7.
📌 Quick Recap — Master These
Before your test, make sure you can confidently do each of the following:
- Explain and apply Special Products.
- Explain and apply Factoring Techniques.
- Explain and apply Rational Algebraic Expressions.
- Explain and apply Worked Example.
Re-read any section above where you hesitate, then try the worked example again without looking.