Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 988 · 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 = 1 and ab = 6, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 11².
3. 3.Use (a − b)² = a² − 2ab + b² to find 51².
4. 4.Use (a + b)(a − b) = a² − b² to find 98 × 82.
5. 5.Use (a + b)² = a² + 2ab + b² to find 98².
6. 6.Use a² − b² = (a + b)(a − b) to find 68² − 57².
7. 7.If a − b = 1 and ab = 20, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 88 × 72.
9. 9.Use (a + b)(a − b) = a² − b² to find 68 × 52.
10. 10.Use (a + b)² = a² + 2ab + b² to find 81².
11. 11.Use a² − b² = (a + b)(a − b) to find 32² − 24².
12. 12.Find the value of x² + 2xy + y² when x = 8 and y = 4.
13. 13.Use a² − b² = (a + b)(a − b) to find 65² − 52².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 67².
16. 16.Use (a + b)² = a² + 2ab + b² to find 101².
17. 17.Use (a + b)(a − b) = a² − b² to find 67 × 53.
18. 18.Use a² − b² = (a + b)(a − b) to find 37² − 29².
19. 19.If a − b = 4 and ab = 5, what is a² + b²?
20. 20.Find the value of x² − 2xy + y² when x = 4 and y = 2.
21. 21.Use (a + b)(a − b) = a² − b² to find 94 × 86.
22. 22.Find the value of x² − 2xy + y² when x = 7 and y = 6.
23. 23.If a − b = 4 and ab = 60, what is a² + b²?
24. 24.If a + b = 11 and ab = 28, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 102².
26. 26.Use (a + b)(a − b) = a² − b² to find 55 × 45.
27. 27.Use (a − b)² = a² − 2ab + b² to find 88².
28. 28.Use (a + b)(a − b) = a² − b² to find 33 × 27.
29. 29.Find the value of x² + 2xy + y² when x = 11 and y = 3.
30. 30.Use (a + b)² = a² + 2ab + b² to find 36².
31. 31.Use (a + b)² = a² + 2ab + b² to find 43².
32. 32.Find the value of x² − 2xy + y² when x = 7 and y = 3.
33. 33.Use (a + b)² = a² + 2ab + b² to find 93².
34. 34.Use (a + b)(a − b) = a² − b² to find 66 × 54.
35. 35.Use a² − b² = (a + b)(a − b) to find 51² − 32².
36. 36.Find the value of x² − y² when x = 15 and y = 5.
37. 37.Use a² − b² = (a + b)(a − b) to find 40² − 2².
38. 38.If a + b = 10 and ab = 16, what is a² + b²?
39. 39.If a + b = 14 and ab = 45, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 89².

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