Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 145 · 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 = 8, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 89² − 66².
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.Use a² − b² = (a + b)(a − b) to find 24² − 14².
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 3.
6. 6.Use (a − b)² = a² − 2ab + b² to find 86².
7. 7.Use a² − b² = (a + b)(a − b) to find 66² − 23².
8. 8.Use (a + b)² = a² + 2ab + b² to find 104².
9. 9.Use (a + b)(a − b) = a² − b² to find 38 × 22.
10. 10.If a + b = 15 and ab = 36, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 62².
12. 12.Use a² − b² = (a + b)(a − b) to find 76² − 8².
13. 13.Use a² − b² = (a + b)(a − b) to find 98² − 67².
14. 14.Use a² − b² = (a + b)(a − b) to find 79² − 1².
15. 15.Use (a + b)(a − b) = a² − b² to find 54 × 46.
16. 16.Find the value of x² − y² when x = 9 and y = 3.
17. 17.Use a² − b² = (a + b)(a − b) to find 73² − 45².
18. 18.If a − b = 8 and ab = 9, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 24².
20. 20.Use a² − b² = (a + b)(a − b) to find 75² − 4².
21. 21.Use (a − b)² = a² − 2ab + b² to find 21².
22. 22.Use (a − b)² = a² − 2ab + b² to find 93².
23. 23.Use (a + b)(a − b) = a² − b² to find 85 × 75.
24. 24.Use (a + b)(a − b) = a² − b² to find 106 × 94.
25. 25.Use (a + b)(a − b) = a² − b² to find 47 × 33.
26. 26.Use a² − b² = (a + b)(a − b) to find 48² − 10².
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 11.
28. 28.Use a² − b² = (a + b)(a − b) to find 68² − 15².
29. 29.Use (a − b)² = a² − 2ab + b² to find 99².
30. 30.Use (a + b)² = a² + 2ab + b² to find 59².
31. 31.Use (a + b)² = a² + 2ab + b² to find 16².
32. 32.Find the value of x² − y² when x = 9 and y = 5.
33. 33.If a + b = 16 and ab = 60, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 67².
35. 35.Use (a − b)² = a² − 2ab + b² to find 72².
36. 36.Use (a + b)(a − b) = a² − b² to find 65 × 55.
37. 37.If a + b = 13 and ab = 30, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 103 × 97.
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 4.
40. 40.Find the value of x² − y² when x = 15 and y = 1.

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