Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 547 · 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)² = a² − 2ab + b² to find 77².
2. 2.Use (a + b)(a − b) = a² − b² to find 106 × 94.
3. 3.Find the value of x² − y² when x = 3 and y = 2.
4. 4.Use (a + b)(a − b) = a² − b² to find 31 × 29.
5. 5.If a − b = 1 and ab = 6, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 36².
7. 7.Use (a + b)² = a² + 2ab + b² to find 104².
8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
9. 9.Use (a − b)² = a² − 2ab + b² to find 47².
10. 10.Use a² − b² = (a + b)(a − b) to find 61² − 30².
11. 11.Use (a + b)(a − b) = a² − b² to find 35 × 25.
12. 12.Use (a − b)² = a² − 2ab + b² to find 78².
13. 13.Find the value of x² + 2xy + y² when x = 3 and y = 1.
14. 14.Use (a − b)² = a² − 2ab + b² to find 91².
15. 15.Use (a − b)² = a² − 2ab + b² to find 53².
16. 16.Use (a + b)(a − b) = a² − b² to find 79 × 61.
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 8.
18. 18.Use (a + b)² = a² + 2ab + b² to find 18².
19. 19.Find the value of x² + 2xy + y² when x = 5 and y = 4.
20. 20.Use (a + b)² = a² + 2ab + b² to find 106².
21. 21.Use (a + b)² = a² + 2ab + b² to find 89².
22. 22.Use a² − b² = (a + b)(a − b) to find 47² − 28².
23. 23.Use (a + b)(a − b) = a² − b² to find 49 × 31.
24. 24.Use (a − b)² = a² − 2ab + b² to find 88².
25. 25.Use (a + b)² = a² + 2ab + b² to find 57².
26. 26.Use (a − b)² = a² − 2ab + b² to find 52².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 42².
29. 29.If a − b = 4 and ab = 96, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 33² − 26².
31. 31.Use (a + b)(a − b) = a² − b² to find 67 × 53.
32. 32.Find the value of x² + 2xy + y² when x = 5 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 37².
34. 34.Use (a + b)² = a² + 2ab + b² to find 26².
35. 35.If a − b = 2 and ab = 3, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 14².
37. 37.Use (a − b)² = a² − 2ab + b² to find 12².
38. 38.If a − b = 2 and ab = 35, what is a² + b²?
39. 39.If a + b = 13 and ab = 12, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 14².

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