Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 45 · 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)(a − b) = a² − b² to find 31 × 29.
2. 2.Use (a + b)(a − b) = a² − b² to find 92 × 88.
3. 3.If a + b = 9 and ab = 20, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 65 × 55.
5. 5.Find the value of x² − y² when x = 7 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 44².
7. 7.If a + b = 15 and ab = 56, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 91².
9. 9.Use a² − b² = (a + b)(a − b) to find 86² − 6².
10. 10.Find the value of x² − 2xy + y² when x = 7 and y = 4.
11. 11.Find the value of x² − y² when x = 13 and y = 7.
12. 12.Use (a + b)(a − b) = a² − b² to find 63 × 57.
13. 13.Use (a + b)(a − b) = a² − b² to find 79 × 61.
14. 14.Use (a − b)² = a² − 2ab + b² to find 34².
15. 15.Find the value of x² + 2xy + y² when x = 12 and y = 10.
16. 16.Use (a + b)(a − b) = a² − b² to find 67 × 53.
17. 17.If a + b = 3 and ab = 2, what is a² + b²?
18. 18.If a + b = 4 and ab = 3, what is a² + b²?
19. 19.If a + b = 17 and ab = 70, what is a² + b²?
20. 20.If a − b = 4 and ab = 32, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 36².
22. 22.Use a² − b² = (a + b)(a − b) to find 27² − 3².
23. 23.Use (a + b)(a − b) = a² − b² to find 39 × 21.
24. 24.Use (a − b)² = a² − 2ab + b² to find 45².
25. 25.Use (a + b)² = a² + 2ab + b² to find 89².
26. 26.Find the value of x² + 2xy + y² when x = 6 and y = 4.
27. 27.Use (a − b)² = a² − 2ab + b² to find 16².
28. 28.Use (a + b)(a − b) = a² − b² to find 23 × 17.
29. 29.Use (a + b)(a − b) = a² − b² to find 78 × 62.
30. 30.Find the value of x² + 2xy + y² when x = 9 and y = 6.
31. 31.Use (a + b)(a − b) = a² − b² to find 101 × 99.
32. 32.Use (a + b)² = a² + 2ab + b² to find 53².
33. 33.Use (a − b)² = a² − 2ab + b² to find 77².
34. 34.If a + b = 14 and ab = 33, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 21 × 19.
36. 36.Use (a + b)² = a² + 2ab + b² to find 65².
37. 37.Use a² − b² = (a + b)(a − b) to find 94² − 71².
38. 38.Use (a + b)² = a² + 2ab + b² to find 11².
39. 39.Find the value of x² − 2xy + y² when x = 3 and y = 1.
40. 40.Use a² − b² = (a + b)(a − b) to find 65² − 11².

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