Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 632 · 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.Find the value of x² − y² when x = 3 and y = 1.
2. 2.If a + b = 23 and ab = 132, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 33² − 12².
4. 4.Use (a + b)² = a² + 2ab + b² to find 83².
5. 5.Use a² − b² = (a + b)(a − b) to find 66² − 55².
6. 6.Use a² − b² = (a + b)(a − b) to find 83² − 72².
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 4 and y = 2.
9. 9.Find the value of x² + 2xy + y² when x = 12 and y = 5.
10. 10.Use (a + b)² = a² + 2ab + b² to find 85².
11. 11.Use (a − b)² = a² − 2ab + b² to find 69².
12. 12.Use (a − b)² = a² − 2ab + b² to find 12².
13. 13.Use (a + b)(a − b) = a² − b² to find 91 × 89.
14. 14.Use (a + b)(a − b) = a² − b² to find 103 × 97.
15. 15.Use (a + b)² = a² + 2ab + b² to find 59².
16. 16.Use (a + b)(a − b) = a² − b² to find 87 × 73.
17. 17.Use (a + b)² = a² + 2ab + b² to find 109².
18. 18.If a − b = 3 and ab = 18, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 108².
20. 20.Use (a + b)(a − b) = a² − b² to find 28 × 12.
21. 21.Use (a + b)(a − b) = a² − b² to find 101 × 99.
22. 22.Find the value of x² + 2xy + y² when x = 9 and y = 2.
23. 23.Use a² − b² = (a + b)(a − b) to find 46² − 42².
24. 24.If a + b = 11 and ab = 18, what is a² + b²?
25. 25.If a + b = 16 and ab = 55, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 13 and y = 12.
27. 27.Find the value of x² − y² when x = 5 and y = 2.
28. 28.Use (a + b)(a − b) = a² − b² to find 51 × 49.
29. 29.Use (a + b)(a − b) = a² − b² to find 61 × 59.
30. 30.Find the value of x² − y² when x = 8 and y = 5.
31. 31.Use (a − b)² = a² − 2ab + b² to find 24².
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 79².
34. 34.Use a² − b² = (a + b)(a − b) to find 62² − 30².
35. 35.Use (a + b)(a − b) = a² − b² to find 23 × 17.
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use (a + b)² = a² + 2ab + b² to find 36².
39. 39.Use (a + b)(a − b) = a² − b² to find 26 × 14.
40. 40.Use (a − b)² = a² − 2ab + b² to find 75².

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