Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 927 · 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 34 × 26.
2. 2.If a + b = 21 and ab = 110, what is a² + b²?
3. 3.If a + b = 15 and ab = 54, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 85².
5. 5.Use (a − b)² = a² − 2ab + b² to find 72².
6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
7. 7.Use (a − b)² = a² − 2ab + b² to find 87².
8. 8.Use (a + b)² = a² + 2ab + b² to find 101².
9. 9.Use a² − b² = (a + b)(a − b) to find 33² − 15².
10. 10.Find the value of x² − y² when x = 15 and y = 3.
11. 11.If a − b = 4 and ab = 45, what is a² + b²?
12. 12.If a + b = 16 and ab = 55, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 61².
14. 14.Use (a + b)² = a² + 2ab + b² to find 71².
15. 15.Use a² − b² = (a + b)(a − b) to find 97² − 72².
16. 16.Use (a + b)² = a² + 2ab + b² to find 94².
17. 17.Use (a − b)² = a² − 2ab + b² to find 66².
18. 18.Use (a − b)² = a² − 2ab + b² to find 56².
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 8.
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 2.
21. 21.Find the value of x² + 2xy + y² when x = 6 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 69².
23. 23.Use (a + b)² = a² + 2ab + b² to find 14².
24. 24.If a + b = 9 and ab = 14, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 3 and y = 1.
26. 26.If a + b = 6 and ab = 8, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 58 × 42.
28. 28.If a − b = 3 and ab = 4, what is a² + b²?
29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 74² − 3².
31. 31.Find the value of x² − 2xy + y² when x = 5 and y = 1.
32. 32.Use a² − b² = (a + b)(a − b) to find 43² − 24².
33. 33.Use a² − b² = (a + b)(a − b) to find 43² − 35².
34. 34.Use a² − b² = (a + b)(a − b) to find 44² − 42².
35. 35.Use (a − b)² = a² − 2ab + b² to find 97².
36. 36.Find the value of x² − 2xy + y² when x = 6 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 30² − 25².
38. 38.Use (a + b)² = a² + 2ab + b² to find 24².
39. 39.If a − b = 1 and ab = 2, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 49 × 31.

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