Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 687 · 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 = 14 and y = 1.
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 91².
4. 4.Find the value of x² − 2xy + y² when x = 3 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 35² − 12².
6. 6.Use a² − b² = (a + b)(a − b) to find 97² − 62².
7. 7.Use (a + b)(a − b) = a² − b² to find 88 × 72.
8. 8.Use (a + b)(a − b) = a² − b² to find 21 × 19.
9. 9.Use (a − b)² = a² − 2ab + b² to find 67².
10. 10.Use (a + b)² = a² + 2ab + b² to find 106².
11. 11.If a − b = 2 and ab = 3, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 43².
13. 13.If a − b = 6 and ab = 16, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 43 × 37.
15. 15.Use a² − b² = (a + b)(a − b) to find 24² − 4².
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.If a + b = 14 and ab = 40, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 15 and y = 12.
19. 19.Use (a − b)² = a² − 2ab + b² to find 17².
20. 20.Use (a + b)(a − b) = a² − b² to find 72 × 68.
21. 21.If a − b = 3 and ab = 54, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 57².
23. 23.Use (a + b)(a − b) = a² − b² to find 63 × 57.
24. 24.Use (a − b)² = a² − 2ab + b² to find 85².
25. 25.Find the value of x² − y² when x = 6 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 84².
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 2.
28. 28.If a − b = 3 and ab = 10, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 37 × 23.
30. 30.Use (a + b)² = a² + 2ab + b² to find 97².
31. 31.Use a² − b² = (a + b)(a − b) to find 47² − 27².
32. 32.Find the value of x² − y² when x = 12 and y = 9.
33. 33.If a + b = 8 and ab = 7, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 93² − 63².
35. 35.Use (a + b)(a − b) = a² − b² to find 106 × 94.
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 2.
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 2.
38. 38.If a + b = 13 and ab = 30, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 51².
40. 40.If a + b = 8 and ab = 15, what is a² + b²?

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