Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 429 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Use (a + b)² = a² + 2ab + b² to find 69².
2. 2.Use (a + b)(a − b) = a² − b² to find 96 × 84.
3. 3.If a + b = 15 and ab = 50, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 106².
5. 5.Use a² − b² = (a + b)(a − b) to find 22² − 7².
6. 6.Use (a + b)² = a² + 2ab + b² to find 27².
7. 7.If a + b = 6 and ab = 8, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 14 and y = 9.
9. 9.Use (a − b)² = a² − 2ab + b² to find 29².
10. 10.Use (a − b)² = a² − 2ab + b² to find 87².
11. 11.Find the value of x² + 2xy + y² when x = 11 and y = 2.
12. 12.Use (a + b)² = a² + 2ab + b² to find 54².
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 2.
14. 14.If a − b = 6 and ab = 7, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 108².
16. 16.Use (a − b)² = a² − 2ab + b² to find 81².
17. 17.Use a² − b² = (a + b)(a − b) to find 65² − 38².
18. 18.Use (a + b)(a − b) = a² − b² to find 35 × 25.
19. 19.Use (a + b)² = a² + 2ab + b² to find 34².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.Use a² − b² = (a + b)(a − b) to find 41² − 33².
22. 22.Use a² − b² = (a + b)(a − b) to find 99² − 82².
23. 23.Find the value of x² − 2xy + y² when x = 9 and y = 6.
24. 24.Use a² − b² = (a + b)(a − b) to find 86² − 22².
25. 25.Use (a − b)² = a² − 2ab + b² to find 14².
26. 26.Use (a + b)² = a² + 2ab + b² to find 21².
27. 27.Use (a − b)² = a² − 2ab + b² to find 56².
28. 28.Use (a − b)² = a² − 2ab + b² to find 52².
29. 29.Use (a + b)(a − b) = a² − b² to find 108 × 92.
30. 30.Find the value of x² + 2xy + y² when x = 12 and y = 10.
31. 31.Use (a + b)(a − b) = a² − b² to find 72 × 68.
32. 32.Use (a + b)² = a² + 2ab + b² to find 16².
33. 33.If a + b = 9 and ab = 14, what is a² + b²?
34. 34.If a + b = 16 and ab = 48, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 99².
36. 36.If a − b = 4 and ab = 21, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 94² − 62².
38. 38.Use (a + b)(a − b) = a² − b² to find 79 × 61.
39. 39.Use (a + b)(a − b) = a² − b² to find 61 × 59.
40. 40.Use a² − b² = (a + b)(a − b) to find 97² − 20².

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