Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 710 · 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 = 14 and y = 11.
2. 2.If a − b = 4 and ab = 5, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 23².
4. 4.Use (a − b)² = a² − 2ab + b² to find 39².
5. 5.If a + b = 10 and ab = 16, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 70² − 51².
7. 7.Use a² − b² = (a + b)(a − b) to find 31² − 11².
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 78².
10. 10.Use (a − b)² = a² − 2ab + b² to find 84².
11. 11.Use (a + b)² = a² + 2ab + b² to find 68².
12. 12.Use (a − b)² = a² − 2ab + b² to find 26².
13. 13.Use (a + b)(a − b) = a² − b² to find 85 × 75.
14. 14.If a − b = 3 and ab = 10, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 93².
16. 16.Find the value of x² − 2xy + y² when x = 7 and y = 6.
17. 17.If a + b = 4 and ab = 3, what is a² + b²?
18. 18.If a − b = 1 and ab = 2, what is a² + b²?
19. 19.If a − b = 4 and ab = 12, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 37².
21. 21.Use a² − b² = (a + b)(a − b) to find 75² − 1².
22. 22.Use (a + b)(a − b) = a² − b² to find 74 × 66.
23. 23.Use (a + b)² = a² + 2ab + b² to find 43².
24. 24.Use (a + b)(a − b) = a² − b² to find 28 × 12.
25. 25.Use (a + b)² = a² + 2ab + b² to find 103².
26. 26.Use (a + b)(a − b) = a² − b² to find 32 × 28.
27. 27.Use a² − b² = (a + b)(a − b) to find 74² − 13².
28. 28.Use (a − b)² = a² − 2ab + b² to find 88².
29. 29.Use a² − b² = (a + b)(a − b) to find 76² − 52².
30. 30.Find the value of x² − 2xy + y² when x = 15 and y = 9.
31. 31.If a + b = 11 and ab = 30, what is a² + b²?
32. 32.If a − b = 3 and ab = 4, what is a² + b²?
33. 33.Find the value of x² − y² when x = 14 and y = 9.
34. 34.Find the value of x² − y² when x = 5 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 86².
36. 36.Use (a − b)² = a² − 2ab + b² to find 44².
37. 37.Use (a − b)² = a² − 2ab + b² to find 79².
38. 38.Use (a − b)² = a² − 2ab + b² to find 56².
39. 39.If a − b = 7 and ab = 30, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 67².

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