Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 190 · 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 68² − 15².
2. 2.Use (a + b)(a − b) = a² − b² to find 33 × 27.
3. 3.Use (a + b)² = a² + 2ab + b² to find 11².
4. 4.If a + b = 9 and ab = 14, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 91² − 89².
6. 6.Use (a + b)(a − b) = a² − b² to find 29 × 11.
7. 7.Use a² − b² = (a + b)(a − b) to find 45² − 30².
8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
9. 9.Use (a − b)² = a² − 2ab + b² to find 79².
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 14.
11. 11.Use (a + b)(a − b) = a² − b² to find 52 × 48.
12. 12.Use a² − b² = (a + b)(a − b) to find 46² − 4².
13. 13.Use (a + b)² = a² + 2ab + b² to find 74².
14. 14.Find the value of x² + 2xy + y² when x = 11 and y = 5.
15. 15.Use (a − b)² = a² − 2ab + b² to find 34².
16. 16.Find the value of x² − y² when x = 8 and y = 5.
17. 17.If a − b = 2 and ab = 3, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 46².
19. 19.Use (a − b)² = a² − 2ab + b² to find 16².
20. 20.Use (a + b)² = a² + 2ab + b² to find 58².
21. 21.Find the value of x² − y² when x = 8 and y = 1.
22. 22.Use (a + b)(a − b) = a² − b² to find 65 × 55.
23. 23.If a + b = 3 and ab = 2, what is a² + b²?
24. 24.Find the value of x² − y² when x = 4 and y = 1.
25. 25.Use (a − b)² = a² − 2ab + b² to find 74².
26. 26.Use (a − b)² = a² − 2ab + b² to find 31².
27. 27.Use (a + b)² = a² + 2ab + b² to find 108².
28. 28.Use (a + b)² = a² + 2ab + b² to find 36².
29. 29.Use (a + b)(a − b) = a² − b² to find 101 × 99.
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.If a + b = 11 and ab = 10, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 72 × 68.
33. 33.Use (a + b)² = a² + 2ab + b² to find 34².
34. 34.Find the value of x² − y² when x = 12 and y = 2.
35. 35.If a − b = 2 and ab = 35, what is a² + b²?
36. 36.Find the value of x² − y² when x = 13 and y = 1.
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Use (a + b)² = a² + 2ab + b² to find 54².
39. 39.If a + b = 7 and ab = 10, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 20².

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