Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 969 · 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 86 × 74.
2. 2.If a + b = 9 and ab = 20, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 92² − 14².
4. 4.Use (a + b)² = a² + 2ab + b² to find 22².
5. 5.Use a² − b² = (a + b)(a − b) to find 52² − 12².
6. 6.Use (a + b)(a − b) = a² − b² to find 57 × 43.
7. 7.Use (a − b)² = a² − 2ab + b² to find 75².
8. 8.Use a² − b² = (a + b)(a − b) to find 56² − 44².
9. 9.Find the value of x² − 2xy + y² when x = 12 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 44².
11. 11.Use (a + b)(a − b) = a² − b² to find 27 × 13.
12. 12.If a − b = 7 and ab = 44, what is a² + b²?
13. 13.Find the value of x² − y² when x = 12 and y = 4.
14. 14.Use (a + b)² = a² + 2ab + b² to find 38².
15. 15.Use (a + b)(a − b) = a² − b² to find 23 × 17.
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 40² − 19².
18. 18.If a + b = 7 and ab = 10, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 1².
20. 20.Use a² − b² = (a + b)(a − b) to find 59² − 53².
21. 21.Use (a + b)² = a² + 2ab + b² to find 63².
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 71 × 69.
24. 24.Use (a + b)² = a² + 2ab + b² to find 85².
25. 25.Use (a + b)² = a² + 2ab + b² to find 16².
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 1.
27. 27.Use (a + b)(a − b) = a² − b² to find 31 × 29.
28. 28.Use (a − b)² = a² − 2ab + b² to find 35².
29. 29.Use (a − b)² = a² − 2ab + b² to find 31².
30. 30.Use (a + b)² = a² + 2ab + b² to find 109².
31. 31.Use (a + b)² = a² + 2ab + b² to find 101².
32. 32.If a − b = 3 and ab = 54, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 97² − 68².
34. 34.If a + b = 15 and ab = 50, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 99².
36. 36.Use (a − b)² = a² − 2ab + b² to find 94².
37. 37.Use (a + b)² = a² + 2ab + b² to find 23².
38. 38.Find the value of x² + 2xy + y² when x = 13 and y = 12.
39. 39.Use (a + b)² = a² + 2ab + b² to find 12².
40. 40.If a − b = 4 and ab = 5, what is a² + b²?

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