Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 191 · 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.If a + b = 10 and ab = 24, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 9.
3. 3.Find the value of x² − y² when x = 7 and y = 6.
4. 4.Use a² − b² = (a + b)(a − b) to find 66² − 42².
5. 5.Use (a + b)² = a² + 2ab + b² to find 83².
6. 6.Use (a + b)(a − b) = a² − b² to find 35 × 25.
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 12 and y = 4.
9. 9.If a − b = 2 and ab = 15, what is a² + b²?
10. 10.If a − b = 1 and ab = 6, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 24².
12. 12.Use (a − b)² = a² − 2ab + b² to find 36².
13. 13.If a + b = 19 and ab = 84, what is a² + b²?
14. 14.Find the value of x² − y² when x = 10 and y = 9.
15. 15.Use (a + b)(a − b) = a² − b² to find 69 × 51.
16. 16.Use a² − b² = (a + b)(a − b) to find 71² − 30².
17. 17.Use (a + b)² = a² + 2ab + b² to find 12².
18. 18.Use a² − b² = (a + b)(a − b) to find 21² − 10².
19. 19.Use a² − b² = (a + b)(a − b) to find 99² − 36².
20. 20.Use a² − b² = (a + b)(a − b) to find 57² − 53².
21. 21.If a − b = 6 and ab = 7, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 58².
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 7.
24. 24.Use (a + b)(a − b) = a² − b² to find 93 × 87.
25. 25.Use a² − b² = (a + b)(a − b) to find 83² − 16².
26. 26.Use (a − b)² = a² − 2ab + b² to find 32².
27. 27.Use (a + b)(a − b) = a² − b² to find 32 × 28.
28. 28.Use (a + b)² = a² + 2ab + b² to find 67².
29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 84 × 76.
31. 31.Use (a + b)(a − b) = a² − b² to find 51 × 49.
32. 32.If a + b = 14 and ab = 48, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 54².
34. 34.Use a² − b² = (a + b)(a − b) to find 43² − 11².
35. 35.Use (a + b)² = a² + 2ab + b² to find 36².
36. 36.Use a² − b² = (a + b)(a − b) to find 21² − 2².
37. 37.Use (a − b)² = a² − 2ab + b² to find 47².
38. 38.Use (a + b)² = a² + 2ab + b² to find 98².
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 85² − 71².

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