Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 101 · 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 81².
2. 2.If a − b = 3 and ab = 108, what is a² + b²?
3. 3.If a + b = 13 and ab = 22, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 51².
5. 5.Use a² − b² = (a + b)(a − b) to find 91² − 68².
6. 6.Use a² − b² = (a + b)(a − b) to find 68² − 15².
7. 7.Use (a + b)² = a² + 2ab + b² to find 12².
8. 8.Use (a + b)² = a² + 2ab + b² to find 31².
9. 9.Use (a + b)² = a² + 2ab + b² to find 22².
10. 10.Find the value of x² + 2xy + y² when x = 13 and y = 11.
11. 11.If a + b = 3 and ab = 2, what is a² + b²?
12. 12.If a − b = 4 and ab = 5, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 17².
14. 14.Find the value of x² + 2xy + y² when x = 15 and y = 6.
15. 15.Use (a + b)(a − b) = a² − b² to find 92 × 88.
16. 16.Use (a + b)² = a² + 2ab + b² to find 43².
17. 17.Use (a + b)(a − b) = a² − b² to find 99 × 81.
18. 18.Use (a + b)² = a² + 2ab + b² to find 88².
19. 19.Find the value of x² + 2xy + y² when x = 14 and y = 9.
20. 20.If a − b = 4 and ab = 21, what is a² + b²?
21. 21.If a + b = 7 and ab = 10, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 109².
24. 24.Use (a + b)(a − b) = a² − b² to find 45 × 35.
25. 25.If a + b = 7 and ab = 6, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 83².
27. 27.Use (a + b)² = a² + 2ab + b² to find 67².
28. 28.Find the value of x² + 2xy + y² when x = 9 and y = 6.
29. 29.Use (a + b)(a − b) = a² − b² to find 91 × 89.
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 7.
31. 31.Use (a − b)² = a² − 2ab + b² to find 78².
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 3.
33. 33.Use (a + b)(a − b) = a² − b² to find 87 × 73.
34. 34.Use (a − b)² = a² − 2ab + b² to find 25².
35. 35.Find the value of x² − 2xy + y² when x = 15 and y = 2.
36. 36.Use (a + b)(a − b) = a² − b² to find 56 × 44.
37. 37.Use (a − b)² = a² − 2ab + b² to find 32².
38. 38.Use (a − b)² = a² − 2ab + b² to find 36².
39. 39.If a − b = 6 and ab = 16, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 2.

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