Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 126 · 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 82 × 78.
2. 2.Use (a − b)² = a² − 2ab + b² to find 96².
3. 3.Use (a − b)² = a² − 2ab + b² to find 44².
4. 4.If a + b = 11 and ab = 24, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Use (a + b)² = a² + 2ab + b² to find 44².
7. 7.Use (a + b)² = a² + 2ab + b² to find 24².
8. 8.Use (a − b)² = a² − 2ab + b² to find 17².
9. 9.If a + b = 18 and ab = 72, what is a² + b²?
10. 10.Find the value of x² − y² when x = 5 and y = 1.
11. 11.Use a² − b² = (a + b)(a − b) to find 92² − 87².
12. 12.Find the value of x² − 2xy + y² when x = 14 and y = 5.
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 3.
14. 14.Use a² − b² = (a + b)(a − b) to find 88² − 34².
15. 15.Use (a + b)² = a² + 2ab + b² to find 92².
16. 16.Find the value of x² − y² when x = 9 and y = 4.
17. 17.Use a² − b² = (a + b)(a − b) to find 63² − 28².
18. 18.Use (a − b)² = a² − 2ab + b² to find 84².
19. 19.If a + b = 5 and ab = 4, what is a² + b²?
20. 20.If a − b = 11 and ab = 12, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 108².
22. 22.Use (a + b)(a − b) = a² − b² to find 102 × 98.
23. 23.Use (a − b)² = a² − 2ab + b² to find 18².
24. 24.If a − b = 1 and ab = 56, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 88 × 72.
26. 26.Use (a + b)² = a² + 2ab + b² to find 95².
27. 27.Use (a + b)(a − b) = a² − b² to find 35 × 25.
28. 28.If a + b = 5 and ab = 6, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 61 × 59.
30. 30.Find the value of x² + 2xy + y² when x = 8 and y = 3.
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.If a − b = 6 and ab = 55, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 31² − 11².
34. 34.Use a² − b² = (a + b)(a − b) to find 32² − 25².
35. 35.Use (a + b)² = a² + 2ab + b² to find 68².
36. 36.Use (a + b)² = a² + 2ab + b² to find 26².
37. 37.Use (a + b)(a − b) = a² − b² to find 93 × 87.
38. 38.Use (a + b)(a − b) = a² − b² to find 49 × 31.
39. 39.Use (a − b)² = a² − 2ab + b² to find 89².
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 3.

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