Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 338 · 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)(a − b) = a² − b² to find 58 × 42.
2. 2.Use (a − b)² = a² − 2ab + b² to find 35².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use (a + b)² = a² + 2ab + b² to find 12².
5. 5.Use (a + b)² = a² + 2ab + b² to find 74².
6. 6.If a + b = 15 and ab = 56, what is a² + b²?
7. 7.If a + b = 14 and ab = 45, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 56².
9. 9.If a + b = 5 and ab = 4, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 29².
11. 11.Use (a − b)² = a² − 2ab + b² to find 47².
12. 12.Find the value of x² − 2xy + y² when x = 3 and y = 1.
13. 13.If a + b = 9 and ab = 18, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 43².
15. 15.Use (a + b)(a − b) = a² − b² to find 68 × 52.
16. 16.Use a² − b² = (a + b)(a − b) to find 75² − 55².
17. 17.Use a² − b² = (a + b)(a − b) to find 75² − 60².
18. 18.If a − b = 2 and ab = 35, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 23 × 17.
20. 20.Use a² − b² = (a + b)(a − b) to find 64² − 54².
21. 21.Use (a − b)² = a² − 2ab + b² to find 28².
22. 22.Use a² − b² = (a + b)(a − b) to find 63² − 6².
23. 23.If a + b = 15 and ab = 54, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 102 × 98.
25. 25.Use (a + b)(a − b) = a² − b² to find 69 × 51.
26. 26.If a + b = 8 and ab = 7, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 94 × 86.
28. 28.Find the value of x² − 2xy + y² when x = 8 and y = 2.
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.If a − b = 1 and ab = 20, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 20² − 16².
32. 32.Use (a + b)(a − b) = a² − b² to find 27 × 13.
33. 33.Use a² − b² = (a + b)(a − b) to find 26² − 9².
34. 34.Use a² − b² = (a + b)(a − b) to find 39² − 7².
35. 35.Use a² − b² = (a + b)(a − b) to find 97² − 28².
36. 36.Use (a + b)² = a² + 2ab + b² to find 33².
37. 37.Use (a + b)(a − b) = a² − b² to find 108 × 92.
38. 38.Use (a + b)(a − b) = a² − b² to find 29 × 11.
39. 39.If a + b = 7 and ab = 12, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 57² − 36².

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