Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 697 · 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 27² − 7².
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 3².
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 34² − 10².
5. 5.Find the value of x² + 2xy + y² when x = 12 and y = 7.
6. 6.Use (a − b)² = a² − 2ab + b² to find 88².
7. 7.Find the value of x² − 2xy + y² when x = 11 and y = 3.
8. 8.Use (a + b)² = a² + 2ab + b² to find 109².
9. 9.Use (a − b)² = a² − 2ab + b² to find 48².
10. 10.Use (a + b)(a − b) = a² − b² to find 58 × 42.
11. 11.If a − b = 3 and ab = 54, what is a² + b²?
12. 12.If a − b = 9 and ab = 10, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 97².
14. 14.Use (a + b)² = a² + 2ab + b² to find 23².
15. 15.Use (a + b)(a − b) = a² − b² to find 54 × 46.
16. 16.If a + b = 11 and ab = 24, what is a² + b²?
17. 17.If a − b = 1 and ab = 20, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 28 × 12.
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 3.
20. 20.If a − b = 4 and ab = 5, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 59².
22. 22.Find the value of x² − 2xy + y² when x = 14 and y = 13.
23. 23.Use a² − b² = (a + b)(a − b) to find 94² − 4².
24. 24.Find the value of x² − y² when x = 3 and y = 1.
25. 25.If a + b = 6 and ab = 5, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 17².
27. 27.Use a² − b² = (a + b)(a − b) to find 75² − 70².
28. 28.Use (a − b)² = a² − 2ab + b² to find 83².
29. 29.Use (a − b)² = a² − 2ab + b² to find 84².
30. 30.Use (a − b)² = a² − 2ab + b² to find 35².
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 33² − 9².
33. 33.Find the value of x² − 2xy + y² when x = 5 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 73 × 67.
35. 35.Use (a + b)(a − b) = a² − b² to find 82 × 78.
36. 36.If a − b = 2 and ab = 8, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 53².
38. 38.Use (a − b)² = a² − 2ab + b² to find 21².
39. 39.If a + b = 13 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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