Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 27 · 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 = 6.
2. 2.Use (a + b)² = a² + 2ab + b² to find 62².
3. 3.Use (a + b)(a − b) = a² − b² to find 99 × 81.
4. 4.Use (a + b)² = a² + 2ab + b² to find 57².
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.Use (a + b)(a − b) = a² − b² to find 29 × 11.
8. 8.If a + b = 11 and ab = 28, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 58² − 40².
10. 10.Use a² − b² = (a + b)(a − b) to find 36² − 4².
11. 11.Use (a + b)(a − b) = a² − b² to find 88 × 72.
12. 12.Use (a + b)² = a² + 2ab + b² to find 65².
13. 13.Use (a − b)² = a² − 2ab + b² to find 36².
14. 14.Use (a − b)² = a² − 2ab + b² to find 97².
15. 15.Find the value of x² − y² when x = 11 and y = 5.
16. 16.If a + b = 18 and ab = 80, what is a² + b²?
17. 17.If a − b = 2 and ab = 120, what is a² + b²?
18. 18.Find the value of x² − y² when x = 14 and y = 11.
19. 19.Use (a + b)(a − b) = a² − b² to find 62 × 58.
20. 20.Use (a + b)² = a² + 2ab + b² to find 55².
21. 21.Use a² − b² = (a + b)(a − b) to find 67² − 14².
22. 22.If a − b = 1 and ab = 20, what is a² + b²?
23. 23.If a + b = 15 and ab = 56, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 64² − 15².
25. 25.Use (a − b)² = a² − 2ab + b² to find 23².
26. 26.Use (a − b)² = a² − 2ab + b² to find 99².
27. 27.Use a² − b² = (a + b)(a − b) to find 68² − 57².
28. 28.If a − b = 4 and ab = 77, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 32 × 28.
30. 30.Use (a + b)² = a² + 2ab + b² to find 12².
31. 31.Use a² − b² = (a + b)(a − b) to find 53² − 30².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.Use (a + b)² = a² + 2ab + b² to find 104².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 44² − 37².
36. 36.Use (a + b)(a − b) = a² − b² to find 75 × 65.
37. 37.If a − b = 1 and ab = 132, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 76² − 14².
39. 39.Find the value of x² − y² when x = 5 and y = 3.
40. 40.Find the value of x² − 2xy + y² when x = 8 and y = 2.

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