Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 733 · 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 27² − 23².
2. 2.Use (a + b)² = a² + 2ab + b² to find 27².
3. 3.If a + b = 17 and ab = 60, what is a² + b²?
4. 4.Find the value of x² − y² when x = 12 and y = 4.
5. 5.Use (a − b)² = a² − 2ab + b² to find 45².
6. 6.Use a² − b² = (a + b)(a − b) to find 57² − 30².
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 79².
9. 9.Use (a + b)(a − b) = a² − b² to find 53 × 47.
10. 10.Use (a − b)² = a² − 2ab + b² to find 85².
11. 11.Find the value of x² − y² when x = 11 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 89 × 71.
13. 13.Use (a − b)² = a² − 2ab + b² to find 62².
14. 14.Use (a + b)² = a² + 2ab + b² to find 65².
15. 15.Use (a + b)² = a² + 2ab + b² to find 24².
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 3.
17. 17.Use (a − b)² = a² − 2ab + b² to find 94².
18. 18.Use a² − b² = (a + b)(a − b) to find 37² − 10².
19. 19.Use a² − b² = (a + b)(a − b) to find 40² − 5².
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 3 and y = 2.
22. 22.Use (a + b)(a − b) = a² − b² to find 45 × 35.
23. 23.Use (a − b)² = a² − 2ab + b² to find 27².
24. 24.Use a² − b² = (a + b)(a − b) to find 23² − 1².
25. 25.Use (a + b)² = a² + 2ab + b² to find 54².
26. 26.Use (a + b)(a − b) = a² − b² to find 27 × 13.
27. 27.Use (a + b)² = a² + 2ab + b² to find 66².
28. 28.Use (a + b)(a − b) = a² − b² to find 92 × 88.
29. 29.Use (a + b)(a − b) = a² − b² to find 51 × 49.
30. 30.If a + b = 5 and ab = 4, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 69² − 18².
32. 32.Use (a − b)² = a² − 2ab + b² to find 16².
33. 33.Find the value of x² − 2xy + y² when x = 3 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 36 × 24.
35. 35.Find the value of x² − 2xy + y² when x = 10 and y = 8.
36. 36.Use (a + b)² = a² + 2ab + b² to find 89².
37. 37.Use a² − b² = (a + b)(a − b) to find 47² − 10².
38. 38.Find the value of x² + 2xy + y² when x = 13 and y = 6.
39. 39.Find the value of x² + 2xy + y² when x = 7 and y = 4.
40. 40.Use (a − b)² = a² − 2ab + b² to find 47².

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