Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 464 · 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 26 × 14.
2. 2.Find the value of x² − 2xy + y² when x = 14 and y = 10.
3. 3.Use (a − b)² = a² − 2ab + b² to find 32².
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 81².
6. 6.Use (a − b)² = a² − 2ab + b² to find 76².
7. 7.Use (a + b)² = a² + 2ab + b² to find 88².
8. 8.Use (a + b)² = a² + 2ab + b² to find 85².
9. 9.Use (a − b)² = a² − 2ab + b² to find 21².
10. 10.If a − b = 2 and ab = 3, what is a² + b²?
11. 11.Find the value of x² − y² when x = 13 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 75² − 27².
13. 13.If a − b = 8 and ab = 33, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 89 × 71.
15. 15.Use a² − b² = (a + b)(a − b) to find 73² − 41².
16. 16.Use a² − b² = (a + b)(a − b) to find 42² − 33².
17. 17.Use a² − b² = (a + b)(a − b) to find 94² − 23².
18. 18.Use a² − b² = (a + b)(a − b) to find 70² − 1².
19. 19.Use (a − b)² = a² − 2ab + b² to find 59².
20. 20.Use (a − b)² = a² − 2ab + b² to find 88².
21. 21.Use (a − b)² = a² − 2ab + b² to find 26².
22. 22.If a − b = 1 and ab = 2, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 96².
24. 24.Use a² − b² = (a + b)(a − b) to find 54² − 40².
25. 25.Use a² − b² = (a + b)(a − b) to find 61² − 44².
26. 26.Use (a − b)² = a² − 2ab + b² to find 78².
27. 27.If a + b = 13 and ab = 36, what is a² + b²?
28. 28.Find the value of x² − y² when x = 9 and y = 5.
29. 29.If a + b = 6 and ab = 5, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 102 × 98.
31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 1.
32. 32.Use a² − b² = (a + b)(a − b) to find 24² − 7².
33. 33.Use (a + b)² = a² + 2ab + b² to find 82².
34. 34.Use (a − b)² = a² − 2ab + b² to find 43².
35. 35.Use (a − b)² = a² − 2ab + b² to find 95².
36. 36.Use (a + b)(a − b) = a² − b² to find 95 × 85.
37. 37.Find the value of x² + 2xy + y² when x = 3 and y = 2.
38. 38.If a − b = 8 and ab = 20, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 35².
40. 40.Use (a − b)² = a² − 2ab + b² to find 75².

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