Mathematics · 2nd preparatory · First Term

Algebra — Factorizing Special Cases

About this lesson

This unit teaches students how to factorize special cases in algebra. It covers recognizing and factorizing perfect square trinomials, the difference of two squares, the sum and difference of two cubes, and using factorization to simplify calculations and solve equations. The unit includes worked examples, self-evaluation exercises, and application problems in contexts such as geometry (areas and volumes), science (pressure formula), technology (data storage), and real-life scenarios like the pyramids of Giza.

Main topics in this lesson

  • Factorizing perfect square trinomials
  • Factorizing the difference of two squares
  • Factorizing the sum and difference of two cubes
  • Using factorization to simplify calculations
  • Solving equations by factorization
  • Applications in geometry, science, and real-life contexts

Key terms and vocabulary

  • Perfect square trinomial
  • Difference between two squares
  • Sum of two cubes
  • Difference between two cubes
  • Factorization

Questions and answers on Algebra — Factorizing Special Cases - practice and revision

Multiple choice questions on this lesson in Mathematics for 2nd preparatory, First Term, with practice exercises for revision and exam preparation.

1

أي مما يلي يمثل تحليلًا كاملًا للمقدار ٢٧س³ − ٨؟

  • 1 (٣س − ٢)(٩س² + ٦س + ٤)
  • 2 (٣س + ٢)(٩س² − ٦س + ٤)
  • 3 (٣س − ٢)(٩س² − ٦س + ٤)
  • 4 (٣س − ٢)³
2

ما حل المعادلة س² + ٨س + ١٦ = ٠؟

  • 1 س = −٤
  • 2 س = ٤
  • 3 س = −٤ أو س = ٤
  • 4 س = ١٦
3

ما حل المعادلة س² − ٩ = ٠؟

  • 1 س = ٣ أو س = −٣
  • 2 س = ٩ أو س = −٩
  • 3 س = ٣ فقط
  • 4 س = ٠ أو س = ٩
4

إذا كانت مساحة مستطيل تساوي س² − ١٦، فما بعداه؟

  • 1 (س − ٤) و(س + ٤)
  • 2 (س − ٤) و(س − ٤)
  • 3 (س + ٤) و(س + ٤)
  • 4 (س − ١٦) و(س + ١)
5

إذا كانت مساحة مربع تساوي س² − ١٤س + ٤٩، فما طول ضلعه؟

  • 1 س − ٧
  • 2 س + ٧
  • 3 س − ٤٩
  • 4 ٧س − ١
6

باستخدام التحليل، ما قيمة ٩٩² − ١²؟

  • 1 ٩٨٠٠
  • 2 ٩٨٠
  • 3 ١٠٠٠٠
  • 4 ٩٨

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