Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 314 · 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 = 16 and ab = 55, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 40² − 12².
3. 3.Use (a − b)² = a² − 2ab + b² to find 42².
4. 4.If a − b = 6 and ab = 7, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 65² − 30².
6. 6.Use (a + b)(a − b) = a² − b² to find 71 × 69.
7. 7.If a − b = 3 and ab = 10, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Find the value of x² + 2xy + y² when x = 9 and y = 4.
10. 10.If a − b = 3 and ab = 4, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 76².
12. 12.If a − b = 5 and ab = 66, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 36².
14. 14.Use (a + b)² = a² + 2ab + b² to find 85².
15. 15.Use (a + b)(a − b) = a² − b² to find 92 × 88.
16. 16.Use (a + b)² = a² + 2ab + b² to find 39².
17. 17.Find the value of x² − y² when x = 12 and y = 9.
18. 18.Use a² − b² = (a + b)(a − b) to find 85² − 24².
19. 19.Use (a − b)² = a² − 2ab + b² to find 52².
20. 20.Use (a + b)² = a² + 2ab + b² to find 106².
21. 21.Use (a − b)² = a² − 2ab + b² to find 41².
22. 22.Use (a + b)² = a² + 2ab + b² to find 33².
23. 23.If a + b = 16 and ab = 63, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 84 × 76.
25. 25.Find the value of x² − y² when x = 14 and y = 9.
26. 26.Use (a + b)(a − b) = a² − b² to find 72 × 68.
27. 27.Find the value of x² − 2xy + y² when x = 15 and y = 10.
28. 28.Use (a − b)² = a² − 2ab + b² to find 38².
29. 29.Use (a + b)² = a² + 2ab + b² to find 12².
30. 30.If a + b = 4 and ab = 3, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 28² − 3².
32. 32.Find the value of x² − 2xy + y² when x = 6 and y = 1.
33. 33.Use a² − b² = (a + b)(a − b) to find 70² − 4².
34. 34.Use (a − b)² = a² − 2ab + b² to find 28².
35. 35.Find the value of x² − y² when x = 9 and y = 2.
36. 36.Find the value of x² − 2xy + y² when x = 4 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 62² − 37².
38. 38.If a − b = 1 and ab = 2, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 37².
40. 40.If a − b = 2 and ab = 24, what is a² + b²?

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