Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 370 · 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 51².
2. 2.Use (a + b)² = a² + 2ab + b² to find 82².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use (a + b)² = a² + 2ab + b² to find 87².
5. 5.Use (a + b)(a − b) = a² − b² to find 59 × 41.
6. 6.Use (a + b)(a − b) = a² − b² to find 83 × 77.
7. 7.Use (a + b)(a − b) = a² − b² to find 26 × 14.
8. 8.Use (a + b)(a − b) = a² − b² to find 44 × 36.
9. 9.Use (a + b)(a − b) = a² − b² to find 29 × 11.
10. 10.Use (a − b)² = a² − 2ab + b² to find 42².
11. 11.Use (a − b)² = a² − 2ab + b² to find 95².
12. 12.Use (a − b)² = a² − 2ab + b² to find 44².
13. 13.Use (a + b)(a − b) = a² − b² to find 51 × 49.
14. 14.Use a² − b² = (a + b)(a − b) to find 75² − 73².
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 8.
16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
17. 17.If a + b = 3 and ab = 2, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 61².
19. 19.If a + b = 12 and ab = 35, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 63².
21. 21.Use a² − b² = (a + b)(a − b) to find 72² − 28².
22. 22.Use (a + b)(a − b) = a² − b² to find 37 × 23.
23. 23.Find the value of x² − 2xy + y² when x = 10 and y = 8.
24. 24.Use (a + b)(a − b) = a² − b² to find 72 × 68.
25. 25.Use a² − b² = (a + b)(a − b) to find 28² − 9².
26. 26.Use (a + b)(a − b) = a² − b² to find 35 × 25.
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 5.
28. 28.Use (a + b)(a − b) = a² − b² to find 57 × 43.
29. 29.If a + b = 8 and ab = 15, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.Use (a + b)² = a² + 2ab + b² to find 26².
32. 32.Use (a − b)² = a² − 2ab + b² to find 39².
33. 33.Use (a + b)² = a² + 2ab + b² to find 72².
34. 34.Use a² − b² = (a + b)(a − b) to find 55² − 29².
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.If a − b = 3 and ab = 54, what is a² + b²?
37. 37.If a − b = 6 and ab = 40, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 7 and y = 6.
39. 39.Use a² − b² = (a + b)(a − b) to find 25² − 24².
40. 40.Find the value of x² − 2xy + y² when x = 15 and y = 3.

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