Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 175 · 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.Find the value of x² − 2xy + y² when x = 12 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 82².
3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 2.
4. 4.Find the value of x² − 2xy + y² when x = 4 and y = 2.
5. 5.Use a² − b² = (a + b)(a − b) to find 78² − 72².
6. 6.Use a² − b² = (a + b)(a − b) to find 22² − 5².
7. 7.Use (a + b)(a − b) = a² − b² to find 107 × 93.
8. 8.Use (a + b)² = a² + 2ab + b² to find 91².
9. 9.Use a² − b² = (a + b)(a − b) to find 49² − 12².
10. 10.Use (a + b)(a − b) = a² − b² to find 58 × 42.
11. 11.Find the value of x² − 2xy + y² when x = 15 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 50² − 46².
13. 13.Use (a − b)² = a² − 2ab + b² to find 38².
14. 14.Use (a + b)(a − b) = a² − b² to find 63 × 57.
15. 15.Find the value of x² + 2xy + y² when x = 14 and y = 7.
16. 16.Use (a + b)² = a² + 2ab + b² to find 48².
17. 17.Use (a + b)² = a² + 2ab + b² to find 37².
18. 18.Use a² − b² = (a + b)(a − b) to find 57² − 48².
19. 19.Use (a + b)(a − b) = a² − b² to find 104 × 96.
20. 20.Use (a + b)(a − b) = a² − b² to find 55 × 45.
21. 21.Use (a + b)² = a² + 2ab + b² to find 35².
22. 22.Use a² − b² = (a + b)(a − b) to find 60² − 47².
23. 23.Use a² − b² = (a + b)(a − b) to find 80² − 37².
24. 24.Use a² − b² = (a + b)(a − b) to find 23² − 16².
25. 25.Use (a − b)² = a² − 2ab + b² to find 23².
26. 26.Use (a + b)² = a² + 2ab + b² to find 46².
27. 27.Use a² − b² = (a + b)(a − b) to find 47² − 36².
28. 28.Use a² − b² = (a + b)(a − b) to find 96² − 85².
29. 29.Find the value of x² − y² when x = 4 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 30² − 5².
31. 31.Use a² − b² = (a + b)(a − b) to find 79² − 75².
32. 32.Find the value of x² − 2xy + y² when x = 6 and y = 4.
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 4.
34. 34.Use (a + b)² = a² + 2ab + b² to find 92².
35. 35.Use (a + b)(a − b) = a² − b² to find 25 × 15.
36. 36.If a − b = 3 and ab = 88, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 72² − 36².
38. 38.Use (a + b)² = a² + 2ab + b² to find 41².
39. 39.Use (a + b)(a − b) = a² − b² to find 91 × 89.
40. 40.Use (a − b)² = a² − 2ab + b² to find 55².

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