Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 225 · 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.Use (a + b)² = a² + 2ab + b² to find 82².
2. 2.Use a² − b² = (a + b)(a − b) to find 97² − 90².
3. 3.Use (a − b)² = a² − 2ab + b² to find 42².
4. 4.Use (a − b)² = a² − 2ab + b² to find 11².
5. 5.If a − b = 2 and ab = 35, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 11 and y = 3.
7. 7.If a + b = 15 and ab = 56, what is a² + b²?
8. 8.If a − b = 7 and ab = 8, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 54 × 46.
10. 10.Use a² − b² = (a + b)(a − b) to find 98² − 24².
11. 11.Use a² − b² = (a + b)(a − b) to find 27² − 18².
12. 12.If a − b = 2 and ab = 3, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 44 × 36.
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.Use a² − b² = (a + b)(a − b) to find 32² − 4².
16. 16.Use (a − b)² = a² − 2ab + b² to find 48².
17. 17.Use (a + b)(a − b) = a² − b² to find 33 × 27.
18. 18.Use a² − b² = (a + b)(a − b) to find 84² − 13².
19. 19.Use (a + b)(a − b) = a² − b² to find 73 × 67.
20. 20.Use (a + b)² = a² + 2ab + b² to find 87².
21. 21.Use (a + b)² = a² + 2ab + b² to find 57².
22. 22.If a + b = 8 and ab = 15, what is a² + b²?
23. 23.Find the value of x² − y² when x = 7 and y = 3.
24. 24.Use (a + b)² = a² + 2ab + b² to find 29².
25. 25.If a + b = 8 and ab = 12, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 16².
27. 27.Use (a − b)² = a² − 2ab + b² to find 66².
28. 28.Use (a − b)² = a² − 2ab + b² to find 67².
29. 29.Use (a − b)² = a² − 2ab + b² to find 45².
30. 30.If a − b = 1 and ab = 72, what is a² + b²?
31. 31.If a − b = 3 and ab = 4, what is a² + b²?
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 23² − 14².
34. 34.Use (a + b)(a − b) = a² − b² to find 21 × 19.
35. 35.If a + b = 9 and ab = 14, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 47².
37. 37.Use a² − b² = (a + b)(a − b) to find 89² − 72².
38. 38.Find the value of x² − y² when x = 5 and y = 3.
39. 39.Use a² − b² = (a + b)(a − b) to find 88² − 13².
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 7².

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