Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 439 · 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)² = a² + 2ab + b² to find 38².
2. 2.Use (a − b)² = a² − 2ab + b² to find 44².
3. 3.Use a² − b² = (a + b)(a − b) to find 26² − 16².
4. 4.Find the value of x² − 2xy + y² when x = 12 and y = 5.
5. 5.If a + b = 6 and ab = 8, what is a² + b²?
6. 6.Find the value of x² − y² when x = 14 and y = 7.
7. 7.Use a² − b² = (a + b)(a − b) to find 79² − 76².
8. 8.If a − b = 1 and ab = 56, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 104².
10. 10.Use a² − b² = (a + b)(a − b) to find 71² − 53².
11. 11.Use (a + b)² = a² + 2ab + b² to find 72².
12. 12.Use (a + b)² = a² + 2ab + b² to find 51².
13. 13.Use (a − b)² = a² − 2ab + b² to find 99².
14. 14.Use (a + b)² = a² + 2ab + b² to find 32².
15. 15.Use (a − b)² = a² − 2ab + b² to find 95².
16. 16.Find the value of x² + 2xy + y² when x = 6 and y = 5.
17. 17.Use (a + b)² = a² + 2ab + b² to find 84².
18. 18.Use (a − b)² = a² − 2ab + b² to find 89².
19. 19.If a + b = 8 and ab = 7, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 19².
21. 21.Use (a − b)² = a² − 2ab + b² to find 35².
22. 22.If a + b = 16 and ab = 63, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 95².
24. 24.Use (a + b)(a − b) = a² − b² to find 82 × 78.
25. 25.Use (a + b)(a − b) = a² − b² to find 78 × 62.
26. 26.Use a² − b² = (a + b)(a − b) to find 49² − 38².
27. 27.Use (a + b)² = a² + 2ab + b² to find 46².
28. 28.Find the value of x² − 2xy + y² when x = 11 and y = 9.
29. 29.Use (a + b)² = a² + 2ab + b² to find 36².
30. 30.Use a² − b² = (a + b)(a − b) to find 33² − 8².
31. 31.Find the value of x² − 2xy + y² when x = 5 and y = 1.
32. 32.Use (a + b)² = a² + 2ab + b² to find 65².
33. 33.Use (a + b)² = a² + 2ab + b² to find 61².
34. 34.Find the value of x² − 2xy + y² when x = 6 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 65 × 55.
36. 36.Use (a + b)(a − b) = a² − b² to find 57 × 43.
37. 37.Use (a + b)² = a² + 2ab + b² to find 78².
38. 38.If a − b = 1 and ab = 30, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 91².
40. 40.Use (a − b)² = a² − 2ab + b² to find 61².

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