Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 436 · 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 53² − 34².
2. 2.Use (a − b)² = a² − 2ab + b² to find 78².
3. 3.Use (a − b)² = a² − 2ab + b² to find 41².
4. 4.If a + b = 7 and ab = 12, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 45².
6. 6.Find the value of x² + 2xy + y² when x = 14 and y = 3.
7. 7.Use a² − b² = (a + b)(a − b) to find 53² − 26².
8. 8.Use (a + b)² = a² + 2ab + b² to find 78².
9. 9.Use (a + b)² = a² + 2ab + b² to find 101².
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.Find the value of x² − y² when x = 14 and y = 3.
12. 12.Use (a + b)(a − b) = a² − b² to find 56 × 44.
13. 13.Find the value of x² − 2xy + y² when x = 7 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 82².
15. 15.Use (a − b)² = a² − 2ab + b² to find 37².
16. 16.If a − b = 3 and ab = 70, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 67².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 69² − 12².
20. 20.If a + b = 11 and ab = 30, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 107².
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 29².
24. 24.Use (a + b)(a − b) = a² − b² to find 106 × 94.
25. 25.Use (a + b)² = a² + 2ab + b² to find 46².
26. 26.Use (a + b)² = a² + 2ab + b² to find 71².
27. 27.Use (a − b)² = a² − 2ab + b² to find 97².
28. 28.Use a² − b² = (a + b)(a − b) to find 46² − 4².
29. 29.Use (a + b)² = a² + 2ab + b² to find 79².
30. 30.Use (a + b)(a − b) = a² − b² to find 41 × 39.
31. 31.Use (a + b)² = a² + 2ab + b² to find 51².
32. 32.Use a² − b² = (a + b)(a − b) to find 81² − 15².
33. 33.Find the value of x² − 2xy + y² when x = 7 and y = 5.
34. 34.Use a² − b² = (a + b)(a − b) to find 72² − 22².
35. 35.Use a² − b² = (a + b)(a − b) to find 43² − 38².
36. 36.Use a² − b² = (a + b)(a − b) to find 22² − 10².
37. 37.Use (a + b)² = a² + 2ab + b² to find 37².
38. 38.Use (a − b)² = a² − 2ab + b² to find 55².
39. 39.Use (a + b)² = a² + 2ab + b² to find 94².
40. 40.Use (a − b)² = a² − 2ab + b² to find 77².

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