Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 981 · 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 42 × 38.
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 3.
3. 3.Use a² − b² = (a + b)(a − b) to find 84² − 77².
4. 4.If a + b = 12 and ab = 35, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 46 × 34.
6. 6.Use (a + b)(a − b) = a² − b² to find 37 × 23.
7. 7.If a + b = 21 and ab = 110, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 36².
9. 9.Find the value of x² − 2xy + y² when x = 8 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 11².
11. 11.Use (a + b)² = a² + 2ab + b² to find 68².
12. 12.Find the value of x² + 2xy + y² when x = 3 and y = 2.
13. 13.Use (a + b)² = a² + 2ab + b² to find 52².
14. 14.Use (a − b)² = a² − 2ab + b² to find 91².
15. 15.If a − b = 1 and ab = 2, what is a² + b²?
16. 16.Find the value of x² − 2xy + y² when x = 13 and y = 2.
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 82².
19. 19.Use (a + b)² = a² + 2ab + b² to find 29².
20. 20.Use (a + b)² = a² + 2ab + b² to find 41².
21. 21.Use (a + b)² = a² + 2ab + b² to find 87².
22. 22.Use (a + b)(a − b) = a² − b² to find 93 × 87.
23. 23.Use (a + b)(a − b) = a² − b² to find 57 × 43.
24. 24.Use (a − b)² = a² − 2ab + b² to find 85².
25. 25.Use (a − b)² = a² − 2ab + b² to find 37².
26. 26.Use a² − b² = (a + b)(a − b) to find 63² − 31².
27. 27.Use (a − b)² = a² − 2ab + b² to find 36².
28. 28.Use a² − b² = (a + b)(a − b) to find 88² − 39².
29. 29.Find the value of x² + 2xy + y² when x = 11 and y = 10.
30. 30.Find the value of x² − y² when x = 4 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 64².
32. 32.Use (a − b)² = a² − 2ab + b² to find 53².
33. 33.Use (a − b)² = a² − 2ab + b² to find 57².
34. 34.Use (a + b)² = a² + 2ab + b² to find 73².
35. 35.Use a² − b² = (a + b)(a − b) to find 93² − 78².
36. 36.Use a² − b² = (a + b)(a − b) to find 35² − 12².
37. 37.Use (a + b)² = a² + 2ab + b² to find 53².
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 8.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 78 × 62.

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