Algebraic Identities

Algebraic identities let you find expressions like a² + b² without knowing a and b themselves.

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1. Q1Hard

   If a + b = 13 and ab = 40, find a² + b².

   1. A129
   2. B97
   3. C89
   4. D249
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   Answer: C. 89

   💡 a² + b² = (a + b)² − 2ab = 169 − 80 = 89.

2. Q2Hard

   If a + b = 9 and ab = 14, find a² + b².

   1. A53
   2. B81
   3. C73
   4. D35
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   Answer: A. 53

   💡 a² + b² = (a + b)² − 2ab = 81 − 28 = 53.

3. Q3Hard

   If a − b = 5 and ab = 36, find a² + b².

   1. A91
   2. B25
   3. C97
   4. D79
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   Answer: C. 97

   💡 a² + b² = (a − b)² + 2ab = 25 + 72 = 97.

4. Q4Hard

   If a + b = 11 and ab = 28, find a² + b².

   1. A93
   2. B65
   3. C71
   4. D177
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   Answer: B. 65

   💡 a² + b² = (a + b)² − 2ab = 121 − 56 = 65.

5. Q5Hard

   If a + b = 3 and ab = 2, find a² + b².

   1. A13
   2. B8
   3. C5
   4. D7
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   Answer: C. 5

   💡 a² + b² = (a + b)² − 2ab = 9 − 4 = 5.

6. Q6Hard

   If a − b = 3 and ab = 4, find a² + b².

   1. A18
   2. B20
   3. C21
   4. D17
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   Answer: D. 17

   💡 a² + b² = (a − b)² + 2ab = 9 + 8 = 17.

7. Q7Hard

   If a − b = 1 and ab = 56, find a² + b².

   1. A113
   2. B119
   3. C57
   4. D123
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   Answer: A. 113

   💡 a² + b² = (a − b)² + 2ab = 1 + 112 = 113.

8. Q8Hard

   If a − b = 1 and ab = 2, find a² + b².

   1. A8
   2. B6
   3. C9
   4. D5
   Show answer

   Answer: D. 5

   💡 a² + b² = (a − b)² + 2ab = 1 + 4 = 5.