Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 49 · 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 89² − 81².
2. 2.If a − b = 7 and ab = 8, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 67² − 64².
4. 4.If a − b = 3 and ab = 28, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 89².
6. 6.Find the value of x² + 2xy + y² when x = 12 and y = 10.
7. 7.Use (a − b)² = a² − 2ab + b² to find 72².
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 25 × 15.
10. 10.Use a² − b² = (a + b)(a − b) to find 93² − 39².
11. 11.Use (a + b)² = a² + 2ab + b² to find 33².
12. 12.Use (a + b)(a − b) = a² − b² to find 39 × 21.
13. 13.Use a² − b² = (a + b)(a − b) to find 89² − 68².
14. 14.Find the value of x² − y² when x = 5 and y = 3.
15. 15.Find the value of x² + 2xy + y² when x = 3 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 12².
17. 17.Use (a + b)² = a² + 2ab + b² to find 31².
18. 18.Use (a + b)(a − b) = a² − b² to find 63 × 57.
19. 19.Use (a + b)(a − b) = a² − b² to find 34 × 26.
20. 20.Use a² − b² = (a + b)(a − b) to find 21² − 7².
21. 21.Use (a + b)² = a² + 2ab + b² to find 58².
22. 22.Use (a + b)² = a² + 2ab + b² to find 76².
23. 23.Use (a + b)² = a² + 2ab + b² to find 104².
24. 24.Find the value of x² + 2xy + y² when x = 7 and y = 5.
25. 25.Use a² − b² = (a + b)(a − b) to find 83² − 16².
26. 26.Use (a + b)² = a² + 2ab + b² to find 37².
27. 27.Use a² − b² = (a + b)(a − b) to find 98² − 25².
28. 28.Use (a + b)(a − b) = a² − b² to find 55 × 45.
29. 29.Use (a + b)² = a² + 2ab + b² to find 77².
30. 30.Use (a + b)² = a² + 2ab + b² to find 66².
31. 31.Use (a + b)² = a² + 2ab + b² to find 81².
32. 32.Find the value of x² − 2xy + y² when x = 14 and y = 6.
33. 33.Use (a + b)² = a² + 2ab + b² to find 43².
34. 34.Use a² − b² = (a + b)(a − b) to find 94² − 18².
35. 35.Find the value of x² − y² when x = 12 and y = 9.
36. 36.Use (a − b)² = a² − 2ab + b² to find 19².
37. 37.Use (a + b)² = a² + 2ab + b² to find 69².
38. 38.Use (a + b)(a − b) = a² − b² to find 107 × 93.
39. 39.Use (a + b)(a − b) = a² − b² to find 96 × 84.
40. 40.If a − b = 4 and ab = 21, what is a² + b²?

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