Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 86 · 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 84².
2. 2.Use a² − b² = (a + b)(a − b) to find 68² − 55².
3. 3.Use a² − b² = (a + b)(a − b) to find 76² − 42².
4. 4.Use (a − b)² = a² − 2ab + b² to find 62².
5. 5.If a − b = 1 and ab = 2, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 12².
7. 7.Use a² − b² = (a + b)(a − b) to find 47² − 16².
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 7.
9. 9.If a + b = 12 and ab = 27, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 87².
11. 11.Use a² − b² = (a + b)(a − b) to find 79² − 73².
12. 12.If a − b = 3 and ab = 88, what is a² + b²?
13. 13.If a − b = 2 and ab = 80, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 36 × 24.
15. 15.Use (a + b)(a − b) = a² − b² to find 29 × 11.
16. 16.Use (a + b)² = a² + 2ab + b² to find 29².
17. 17.Use (a + b)² = a² + 2ab + b² to find 68².
18. 18.Use (a + b)(a − b) = a² − b² to find 45 × 35.
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use (a + b)(a − b) = a² − b² to find 71 × 69.
21. 21.Find the value of x² − 2xy + y² when x = 6 and y = 2.
22. 22.Use (a + b)² = a² + 2ab + b² to find 74².
23. 23.Find the value of x² + 2xy + y² when x = 5 and y = 4.
24. 24.Use (a − b)² = a² − 2ab + b² to find 32².
25. 25.Use (a + b)² = a² + 2ab + b² to find 28².
26. 26.Find the value of x² + 2xy + y² when x = 3 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 21².
28. 28.Use (a − b)² = a² − 2ab + b² to find 88².
29. 29.Use a² − b² = (a + b)(a − b) to find 75² − 10².
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.Use a² − b² = (a + b)(a − b) to find 71² − 53².
32. 32.Find the value of x² − 2xy + y² when x = 9 and y = 8.
33. 33.Use a² − b² = (a + b)(a − b) to find 69² − 51².
34. 34.Use (a − b)² = a² − 2ab + b² to find 39².
35. 35.Use a² − b² = (a + b)(a − b) to find 31² − 7².
36. 36.Use a² − b² = (a + b)(a − b) to find 91² − 75².
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use (a + b)² = a² + 2ab + b² to find 96².
39. 39.Use a² − b² = (a + b)(a − b) to find 60² − 1².
40. 40.Use a² − b² = (a + b)(a − b) to find 45² − 40².

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