Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 147 · 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 = 3 and ab = 2, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 66².
3. 3.Use (a − b)² = a² − 2ab + b² to find 72².
4. 4.Use (a + b)² = a² + 2ab + b² to find 83².
5. 5.Use (a − b)² = a² − 2ab + b² to find 35².
6. 6.Use a² − b² = (a + b)(a − b) to find 79² − 44².
7. 7.Use (a + b)² = a² + 2ab + b² to find 14².
8. 8.Use (a − b)² = a² − 2ab + b² to find 65².
9. 9.Use (a + b)(a − b) = a² − b² to find 81 × 79.
10. 10.Use (a + b)(a − b) = a² − b² to find 42 × 38.
11. 11.If a − b = 1 and ab = 2, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 14 and y = 9.
13. 13.Use (a + b)² = a² + 2ab + b² to find 12².
14. 14.Find the value of x² + 2xy + y² when x = 4 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 45².
16. 16.Use (a − b)² = a² − 2ab + b² to find 11².
17. 17.Use a² − b² = (a + b)(a − b) to find 66² − 51².
18. 18.Use (a + b)(a − b) = a² − b² to find 73 × 67.
19. 19.Use (a + b)² = a² + 2ab + b² to find 11².
20. 20.Find the value of x² − y² when x = 14 and y = 1.
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 3.
22. 22.Use (a + b)(a − b) = a² − b² to find 23 × 17.
23. 23.Use (a + b)(a − b) = a² − b² to find 61 × 59.
24. 24.Find the value of x² + 2xy + y² when x = 7 and y = 1.
25. 25.If a + b = 7 and ab = 6, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 54².
27. 27.If a + b = 16 and ab = 63, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 67².
29. 29.Find the value of x² − 2xy + y² when x = 9 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 35 × 25.
31. 31.Use (a + b)(a − b) = a² − b² to find 57 × 43.
32. 32.Use (a + b)² = a² + 2ab + b² to find 23².
33. 33.Use a² − b² = (a + b)(a − b) to find 20² − 7².
34. 34.Find the value of x² − 2xy + y² when x = 5 and y = 2.
35. 35.Use (a + b)² = a² + 2ab + b² to find 81².
36. 36.Use a² − b² = (a + b)(a − b) to find 55² − 9².
37. 37.Use (a − b)² = a² − 2ab + b² to find 36².
38. 38.Use (a − b)² = a² − 2ab + b² to find 75².
39. 39.If a − b = 3 and ab = 4, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 1.

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