Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 157 · 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 59 × 41.
2. 2.Use (a + b)(a − b) = a² − b² to find 82 × 78.
3. 3.Find the value of x² − 2xy + y² when x = 6 and y = 5.
4. 4.Use (a − b)² = a² − 2ab + b² to find 85².
5. 5.If a + b = 19 and ab = 88, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 42².
7. 7.Use a² − b² = (a + b)(a − b) to find 68² − 10².
8. 8.Use (a + b)(a − b) = a² − b² to find 109 × 91.
9. 9.Use (a + b)² = a² + 2ab + b² to find 25².
10. 10.Find the value of x² − 2xy + y² when x = 5 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Use (a + b)² = a² + 2ab + b² to find 81².
13. 13.If a + b = 3 and ab = 2, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 67².
15. 15.Use (a + b)² = a² + 2ab + b² to find 22².
16. 16.Use (a + b)² = a² + 2ab + b² to find 28².
17. 17.Use (a − b)² = a² − 2ab + b² to find 57².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 1.
19. 19.Use (a + b)(a − b) = a² − b² to find 29 × 11.
20. 20.If a + b = 18 and ab = 80, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 24².
22. 22.Use (a + b)(a − b) = a² − b² to find 96 × 84.
23. 23.If a + b = 11 and ab = 24, what is a² + b²?
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 5.
25. 25.Use (a − b)² = a² − 2ab + b² to find 59².
26. 26.If a + b = 10 and ab = 24, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 12 and y = 5.
28. 28.Find the value of x² − 2xy + y² when x = 14 and y = 7.
29. 29.Use (a + b)(a − b) = a² − b² to find 92 × 88.
30. 30.Use a² − b² = (a + b)(a − b) to find 26² − 20².
31. 31.Use (a + b)(a − b) = a² − b² to find 31 × 29.
32. 32.Use (a − b)² = a² − 2ab + b² to find 52².
33. 33.If a − b = 2 and ab = 15, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 21² − 6².
35. 35.Use (a + b)(a − b) = a² − b² to find 107 × 93.
36. 36.Use (a − b)² = a² − 2ab + b² to find 74².
37. 37.Use (a − b)² = a² − 2ab + b² to find 96².
38. 38.Use (a + b)² = a² + 2ab + b² to find 34².
39. 39.If a − b = 3 and ab = 10, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 13 and y = 1.

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