Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 33 · 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.Find the value of x² + 2xy + y² when x = 8 and y = 5.
2. 2.Find the value of x² − y² when x = 11 and y = 4.
3. 3.Use (a + b)² = a² + 2ab + b² to find 91².
4. 4.Find the value of x² − 2xy + y² when x = 9 and y = 1.
5. 5.Use (a − b)² = a² − 2ab + b² to find 48².
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 78².
7. 7.Use a² − b² = (a + b)(a − b) to find 72² − 52².
8. 8.Use a² − b² = (a + b)(a − b) to find 61² − 39².
9. 9.Use (a + b)(a − b) = a² − b² to find 48 × 32.
10. 10.Use (a − b)² = a² − 2ab + b² to find 24².
11. 11.Find the value of x² − 2xy + y² when x = 5 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 67² − 18².
13. 13.Use (a + b)(a − b) = a² − b² to find 94 × 86.
14. 14.Use (a − b)² = a² − 2ab + b² to find 41².
15. 15.Use (a + b)² = a² + 2ab + b² to find 97².
16. 16.Find the value of x² − y² when x = 13 and y = 4.
17. 17.If a + b = 11 and ab = 30, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use (a + b)² = a² + 2ab + b² to find 42².
20. 20.Use a² − b² = (a + b)(a − b) to find 58² − 12².
21. 21.Find the value of x² + 2xy + y² when x = 13 and y = 10.
22. 22.Use (a + b)(a − b) = a² − b² to find 104 × 96.
23. 23.Use (a + b)² = a² + 2ab + b² to find 38².
24. 24.Find the value of x² − 2xy + y² when x = 14 and y = 7.
25. 25.Use (a + b)(a − b) = a² − b² to find 37 × 23.
26. 26.Use (a − b)² = a² − 2ab + b² to find 93².
27. 27.Find the value of x² − y² when x = 9 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 74².
29. 29.Use (a − b)² = a² − 2ab + b² to find 44².
30. 30.Use (a + b)² = a² + 2ab + b² to find 13².
31. 31.Use (a + b)² = a² + 2ab + b² to find 58².
32. 32.Use a² − b² = (a + b)(a − b) to find 45² − 22².
33. 33.Use (a + b)² = a² + 2ab + b² to find 68².
34. 34.Use (a − b)² = a² − 2ab + b² to find 47².
35. 35.Use (a − b)² = a² − 2ab + b² to find 15².
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 35 × 25.
38. 38.Use (a + b)(a − b) = a² − b² to find 105 × 95.
39. 39.If a + b = 14 and ab = 24, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 89².

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