Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 574 · 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 57² − 10².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.If a + b = 13 and ab = 22, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 68 × 52.
5. 5.If a − b = 3 and ab = 40, what is a² + b²?
6. 6.If a − b = 1 and ab = 72, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 24².
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.If a − b = 3 and ab = 4, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 91².
11. 11.If a − b = 1 and ab = 6, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 97².
13. 13.Use (a − b)² = a² − 2ab + b² to find 45².
14. 14.Use (a − b)² = a² − 2ab + b² to find 89².
15. 15.Use a² − b² = (a + b)(a − b) to find 96² − 79².
16. 16.Use (a − b)² = a² − 2ab + b² to find 21².
17. 17.If a + b = 11 and ab = 28, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 35 × 25.
19. 19.Use (a − b)² = a² − 2ab + b² to find 84².
20. 20.Use (a + b)² = a² + 2ab + b² to find 48².
21. 21.Use a² − b² = (a + b)(a − b) to find 67² − 36².
22. 22.Use (a − b)² = a² − 2ab + b² to find 93².
23. 23.Use (a + b)(a − b) = a² − b² to find 87 × 73.
24. 24.Use a² − b² = (a + b)(a − b) to find 78² − 36².
25. 25.Use a² − b² = (a + b)(a − b) to find 83² − 2².
26. 26.If a + b = 14 and ab = 24, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 61 × 59.
28. 28.Use (a + b)(a − b) = a² − b² to find 24 × 16.
29. 29.Use (a − b)² = a² − 2ab + b² to find 59².
30. 30.Use a² − b² = (a + b)(a − b) to find 44² − 37².
31. 31.Use (a + b)² = a² + 2ab + b² to find 46².
32. 32.Use a² − b² = (a + b)(a − b) to find 82² − 10².
33. 33.If a + b = 10 and ab = 16, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 59² − 10².
35. 35.Use (a + b)(a − b) = a² − b² to find 98 × 82.
36. 36.Use (a + b)(a − b) = a² − b² to find 25 × 15.
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 83².
39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 6.
40. 40.Use (a − b)² = a² − 2ab + b² to find 69².

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