Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 80 · 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 58² − 24².
2. 2.Use a² − b² = (a + b)(a − b) to find 36² − 7².
3. 3.Use (a + b)² = a² + 2ab + b² to find 99².
4. 4.Use (a − b)² = a² − 2ab + b² to find 46².
5. 5.Use a² − b² = (a + b)(a − b) to find 30² − 12².
6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
7. 7.Use (a + b)(a − b) = a² − b² to find 63 × 57.
8. 8.Use (a + b)(a − b) = a² − b² to find 36 × 24.
9. 9.Find the value of x² − y² when x = 4 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 25².
11. 11.Use a² − b² = (a + b)(a − b) to find 76² − 12².
12. 12.Use a² − b² = (a + b)(a − b) to find 47² − 25².
13. 13.Use (a + b)(a − b) = a² − b² to find 37 × 23.
14. 14.If a + b = 9 and ab = 20, what is a² + b²?
15. 15.If a + b = 10 and ab = 24, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 28² − 14².
17. 17.Use (a + b)(a − b) = a² − b² to find 92 × 88.
18. 18.Use (a + b)² = a² + 2ab + b² to find 109².
19. 19.Use (a + b)(a − b) = a² − b² to find 42 × 38.
20. 20.Use (a − b)² = a² − 2ab + b² to find 12².
21. 21.If a + b = 6 and ab = 8, what is a² + b²?
22. 22.Find the value of x² − y² when x = 15 and y = 4.
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 42².
25. 25.If a − b = 1 and ab = 12, what is a² + b²?
26. 26.If a − b = 5 and ab = 14, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 15².
28. 28.Use (a + b)² = a² + 2ab + b² to find 57².
29. 29.Use (a + b)² = a² + 2ab + b² to find 32².
30. 30.Use (a − b)² = a² − 2ab + b² to find 26².
31. 31.Use a² − b² = (a + b)(a − b) to find 73² − 10².
32. 32.Find the value of x² − y² when x = 13 and y = 11.
33. 33.Use a² − b² = (a + b)(a − b) to find 64² − 24².
34. 34.Use (a + b)² = a² + 2ab + b² to find 14².
35. 35.Use a² − b² = (a + b)(a − b) to find 46² − 27².
36. 36.If a + b = 12 and ab = 32, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 91².
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 2.
39. 39.Use a² − b² = (a + b)(a − b) to find 80² − 20².
40. 40.Use a² − b² = (a + b)(a − b) to find 25² − 20².

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