Free worksheet
Exploring Algebraic Identities · Class 9
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Exploring Algebraic Identities · English
Name: ____________________Date: ____________
Questions
Use (a + b)² = a² + 2ab + b² to find 103².
Use (a − b)(a + b) = a² − b² to find 98 × 102.
If a + b = 7 and ab = 10, what is a² + b²?
Answer key
- 10609 — (100 + 3)² = 10,000 + 600 + 9 = 10,609.
- 9996 — (100 − 2)(100 + 2) = 10,000 − 4 = 9,996.
- 29 — a² + b² = (a + b)² − 2ab = 49 − 20 = 29.
बीजीय सर्वसमिकाओं की खोज · हिन्दी
नाम: ____________________तारीख़: ____________
प्रश्न
(a + b)² = a² + 2ab + b² से 103² ज्ञात करो।
(a − b)(a + b) = a² − b² से 98 × 102 ज्ञात करो।
अगर a + b = 7 और ab = 10 है, तो a² + b² कितना है?
उत्तर
- 10609 — (100 + 3)² = 10,000 + 600 + 9 = 10,609।
- 9996 — (100 − 2)(100 + 2) = 10,000 − 4 = 9,996।
- 29 — a² + b² = (a + b)² − 2ab = 49 − 20 = 29।
बैजिक नित्यसमानतांचा शोध · मराठी
नाव: ____________________दिनांक: ____________
प्रश्न
(a + b)² = a² + 2ab + b² वापरून 103² काढा.
(a − b)(a + b) = a² − b² वापरून 98 × 102 काढा.
जर a + b = 7 आणि ab = 10 असेल, तर a² + b² किती?
उत्तरे
- 10609 — (100 + 3)² = 10,000 + 600 + 9 = 10,609.
- 9996 — (100 − 2)(100 + 2) = 10,000 − 4 = 9,996.
- 29 — a² + b² = (a + b)² − 2ab = 49 − 20 = 29.
A worked example
If a − b = 3 and ab = 28, find a² + b².
- Use (a − b)² = a² − 2ab + b², so a² + b² = (a − b)² + 2ab.
- a² + b² = 3² + 2 × 28 = 9 + 56 = 65.
Answer: a² + b² = 65. Check: a = 7 and b = 4 fit (7 − 4 = 3, 7 × 4 = 28), and 49 + 16 = 65.
The common mistake
Writing (a + b)² = a² + b² and dropping the middle term 2ab. Test it with a = b = 1: (1 + 1)² = 4, but 1² + 1² = 2.
In the NCERT book
Ganita Manjari Part I, Class 9 (First Edition April 2026), Chapter 4: Exploring Algebraic Identities, pages 68 to 91. Open the chapter (PDF).
Practise this topic online: 5 questions, marked as you go, with a hint after a wrong answer.
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