Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 811 · 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 = 9 and ab = 14, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 46² − 21².
3. 3.Use (a + b)(a − b) = a² − b² to find 75 × 65.
4. 4.Use (a + b)² = a² + 2ab + b² to find 32².
5. 5.Use (a + b)² = a² + 2ab + b² to find 46².
6. 6.Use (a + b)² = a² + 2ab + b² to find 106².
7. 7.Use a² − b² = (a + b)(a − b) to find 21² − 13².
8. 8.Use (a + b)(a − b) = a² − b² to find 32 × 28.
9. 9.Use (a − b)² = a² − 2ab + b² to find 77².
10. 10.Use (a + b)(a − b) = a² − b² to find 89 × 71.
11. 11.Use (a + b)(a − b) = a² − b² to find 33 × 27.
12. 12.Use (a + b)² = a² + 2ab + b² to find 36².
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 1.
14. 14.Use (a − b)² = a² − 2ab + b² to find 86².
15. 15.Use a² − b² = (a + b)(a − b) to find 48² − 18².
16. 16.Use (a + b)² = a² + 2ab + b² to find 14².
17. 17.If a − b = 10 and ab = 11, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 55².
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use (a + b)(a − b) = a² − b² to find 54 × 46.
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Use a² − b² = (a + b)(a − b) to find 51² − 36².
24. 24.If a + b = 6 and ab = 5, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 51².
26. 26.Use (a + b)² = a² + 2ab + b² to find 101².
27. 27.Use a² − b² = (a + b)(a − b) to find 68² − 5².
28. 28.Use (a + b)² = a² + 2ab + b² to find 29².
29. 29.If a + b = 13 and ab = 40, what is a² + b²?
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 85².
32. 32.Find the value of x² + 2xy + y² when x = 10 and y = 2.
33. 33.Find the value of x² − y² when x = 15 and y = 14.
34. 34.Use (a + b)² = a² + 2ab + b² to find 22².
35. 35.If a − b = 1 and ab = 56, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 74².
37. 37.Use (a + b)(a − b) = a² − b² to find 62 × 58.
38. 38.If a − b = 9 and ab = 22, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 99 × 81.
40. 40.Find the value of x² − y² when x = 8 and y = 4.

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