Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 122 · 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 a² − b² = (a + b)(a − b) to find 63² − 16².
2. 2.If a − b = 3 and ab = 70, what is a² + b²?
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 97² − 35².
5. 5.Find the value of x² + 2xy + y² when x = 8 and y = 2.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 87 × 73.
8. 8.If a + b = 15 and ab = 56, what is a² + b²?
9. 9.If a − b = 11 and ab = 12, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 59².
11. 11.Use (a + b)(a − b) = a² − b² to find 21 × 19.
12. 12.Use (a + b)² = a² + 2ab + b² to find 54².
13. 13.Use (a − b)² = a² − 2ab + b² to find 92².
14. 14.Use a² − b² = (a + b)(a − b) to find 33² − 6².
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 6².
16. 16.Use (a + b)² = a² + 2ab + b² to find 105².
17. 17.If a + b = 13 and ab = 12, what is a² + b²?
18. 18.Find the value of x² − y² when x = 8 and y = 3.
19. 19.Use (a + b)(a − b) = a² − b² to find 22 × 18.
20. 20.Use (a + b)² = a² + 2ab + b² to find 36².
21. 21.Use (a + b)² = a² + 2ab + b² to find 25².
22. 22.Use (a + b)(a − b) = a² − b² to find 102 × 98.
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.If a − b = 6 and ab = 7, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 57².
26. 26.Use a² − b² = (a + b)(a − b) to find 76² − 67².
27. 27.Use a² − b² = (a + b)(a − b) to find 76² − 2².
28. 28.Use (a + b)(a − b) = a² − b² to find 88 × 72.
29. 29.Use (a + b)² = a² + 2ab + b² to find 12².
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 109².
32. 32.Use (a + b)² = a² + 2ab + b² to find 103².
33. 33.Use (a + b)² = a² + 2ab + b² to find 87².
34. 34.Use (a − b)² = a² − 2ab + b² to find 23².
35. 35.Use (a − b)² = a² − 2ab + b² to find 98².
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 2.
37. 37.Use (a − b)² = a² − 2ab + b² to find 71².
38. 38.Use (a + b)(a − b) = a² − b² to find 51 × 49.
39. 39.Use a² − b² = (a + b)(a − b) to find 84² − 4².
40. 40.Use (a + b)² = a² + 2ab + b² to find 84².

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