Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 110 · 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 85² − 4².
2. 2.Use (a + b)(a − b) = a² − b² to find 94 × 86.
3. 3.Use (a + b)(a − b) = a² − b² to find 75 × 65.
4. 4.Use (a + b)² = a² + 2ab + b² to find 23².
5. 5.Use (a − b)² = a² − 2ab + b² to find 44².
6. 6.Use (a + b)² = a² + 2ab + b² to find 44².
7. 7.Use (a + b)² = a² + 2ab + b² to find 88².
8. 8.Use a² − b² = (a + b)(a − b) to find 98² − 32².
9. 9.Use (a + b)² = a² + 2ab + b² to find 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 60² − 44².
11. 11.Use (a + b)(a − b) = a² − b² to find 23 × 17.
12. 12.If a − b = 10 and ab = 11, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 86² − 39².
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 1.
15. 15.Use (a + b)(a − b) = a² − b² to find 73 × 67.
16. 16.Find the value of x² + 2xy + y² when x = 3 and y = 1.
17. 17.Find the value of x² + 2xy + y² when x = 7 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 12².
19. 19.Use a² − b² = (a + b)(a − b) to find 23² − 6².
20. 20.If a + b = 5 and ab = 4, what is a² + b²?
21. 21.Find the value of x² − y² when x = 14 and y = 6.
22. 22.Use (a + b)² = a² + 2ab + b² to find 52².
23. 23.Find the value of x² − 2xy + y² when x = 12 and y = 4.
24. 24.Find the value of x² − 2xy + y² when x = 10 and y = 6.
25. 25.Use (a − b)² = a² − 2ab + b² to find 24².
26. 26.Find the value of x² − 2xy + y² when x = 14 and y = 13.
27. 27.Find the value of x² − 2xy + y² when x = 6 and y = 4.
28. 28.Find the value of x² − 2xy + y² when x = 3 and y = 2.
29. 29.If a − b = 2 and ab = 8, what is a² + b²?
30. 30.Find the value of x² − y² when x = 6 and y = 4.
31. 31.Use (a + b)(a − b) = a² − b² to find 58 × 42.
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 77 × 63.
34. 34.Find the value of x² − y² when x = 3 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 38².
36. 36.Use (a − b)² = a² − 2ab + b² to find 13².
37. 37.Use (a + b)² = a² + 2ab + b² to find 69².
38. 38.Use (a − b)² = a² − 2ab + b² to find 65².
39. 39.If a − b = 2 and ab = 3, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 99² − 45².

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