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Class 9–10 Maths: Algebraic identities practice questions

Practise algebraic identities for Classes 9 and 10. Try the 10-question quiz below and see each answer explained straight away, then read all 12 worked examples with answers underneath. Free, no sign-up.

Algebraic identities: worked examples with answers

These Maths questions are generated, so a fresh set appears every time you press "Practise more questions". Here are some worked examples.

1. If a + b = 15 and ab = 24, what is a² + b²?

   1. A. 201
   2. B. 48
   3. C. 177 ✓
   4. D. 179

   Answer: 177. (a + b)² = a² + 2ab + b², so a² + b² = 15² − 2 × 24 = 225 − 48 = 177.

2. If a + b = 15 and ab = 17, what is a² + b²?

   1. A. 193
   2. B. 191 ✓
   3. C. 225
   4. D. 259

   Answer: 191. (a + b)² = a² + 2ab + b², so a² + b² = 15² − 2 × 17 = 225 − 34 = 191.

3. If a + b = 9 and ab = 7, what is a² + b²?

   1. A. 69
   2. B. 14
   3. C. 67 ✓
   4. D. 74

   Answer: 67. (a + b)² = a² + 2ab + b², so a² + b² = 9² − 2 × 7 = 81 − 14 = 67.

4. If a + b = 8 and ab = 12, what is a² + b²?

   1. A. 40 ✓
   2. B. 24
   3. C. 88
   4. D. 42

   Answer: 40. (a + b)² = a² + 2ab + b², so a² + b² = 8² − 2 × 12 = 64 − 24 = 40.

5. If a + b = 11 and ab = 12, what is a² + b²?

   1. A. 121
   2. B. 97 ✓
   3. C. 145
   4. D. 109

   Answer: 97. (a + b)² = a² + 2ab + b², so a² + b² = 11² − 2 × 12 = 121 − 24 = 97.

6. If a + b = 6 and ab = 7, what is a² + b²?

   1. A. 22 ✓
   2. B. 14
   3. C. 29
   4. D. 24

   Answer: 22. (a + b)² = a² + 2ab + b², so a² + b² = 6² − 2 × 7 = 36 − 14 = 22.

7. If a + b = 13 and ab = 26, what is a² + b²?

   1. A. 52
   2. B. 117 ✓
   3. C. 119
   4. D. 169

   Answer: 117. (a + b)² = a² + 2ab + b², so a² + b² = 13² − 2 × 26 = 169 − 52 = 117.

8. If a + b = 12 and ab = 26, what is a² + b²?

   1. A. 196
   2. B. 92 ✓
   3. C. 144
   4. D. 52

   Answer: 92. (a + b)² = a² + 2ab + b², so a² + b² = 12² − 2 × 26 = 144 − 52 = 92.

9. If a + b = 8 and ab = 13, what is a² + b²?

   1. A. 90
   2. B. 40
   3. C. 38 ✓
   4. D. 51

   Answer: 38. (a + b)² = a² + 2ab + b², so a² + b² = 8² − 2 × 13 = 64 − 26 = 38.

10. If a + b = 7 and ab = 10, what is a² + b²?

    1. A. 20
    2. B. 29 ✓
    3. C. 31
    4. D. 69

    Answer: 29. (a + b)² = a² + 2ab + b², so a² + b² = 7² − 2 × 10 = 49 − 20 = 29.

11. If a + b = 8 and ab = 9, what is a² + b²?

    1. A. 48
    2. B. 64
    3. C. 18
    4. D. 46 ✓

    Answer: 46. (a + b)² = a² + 2ab + b², so a² + b² = 8² − 2 × 9 = 64 − 18 = 46.

12. If a + b = 11 and ab = 11, what is a² + b²?

    1. A. 22
    2. B. 110
    3. C. 121
    4. D. 99 ✓

    Answer: 99. (a + b)² = a² + 2ab + b², so a² + b² = 11² − 2 × 11 = 121 − 22 = 99.

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