Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 573 · 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)(a − b) = a² − b² to find 38 × 22.
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.Use (a + b)(a − b) = a² − b² to find 105 × 95.
4. 4.Use a² − b² = (a + b)(a − b) to find 64² − 3².
5. 5.Find the value of x² + 2xy + y² when x = 14 and y = 7.
6. 6.Use (a + b)(a − b) = a² − b² to find 107 × 93.
7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 1.
8. 8.Use (a + b)² = a² + 2ab + b² to find 14².
9. 9.Use a² − b² = (a + b)(a − b) to find 44² − 2².
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 5².
11. 11.Use (a − b)² = a² − 2ab + b² to find 75².
12. 12.Use (a − b)² = a² − 2ab + b² to find 22².
13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
14. 14.Use (a + b)(a − b) = a² − b² to find 103 × 97.
15. 15.Use (a + b)(a − b) = a² − b² to find 76 × 64.
16. 16.Use (a + b)² = a² + 2ab + b² to find 44².
17. 17.Use (a − b)² = a² − 2ab + b² to find 24².
18. 18.If a + b = 10 and ab = 21, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 56².
20. 20.Use (a + b)² = a² + 2ab + b² to find 36².
21. 21.Use a² − b² = (a + b)(a − b) to find 66² − 56².
22. 22.If a + b = 11 and ab = 30, what is a² + b²?
23. 23.If a + b = 5 and ab = 6, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 62².
25. 25.Use (a + b)² = a² + 2ab + b² to find 26².
26. 26.Use (a + b)(a − b) = a² − b² to find 66 × 54.
27. 27.Use a² − b² = (a + b)(a − b) to find 24² − 14².
28. 28.Find the value of x² − 2xy + y² when x = 5 and y = 4.
29. 29.Use (a − b)² = a² − 2ab + b² to find 67².
30. 30.If a − b = 1 and ab = 30, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 42².
32. 32.Find the value of x² − y² when x = 3 and y = 1.
33. 33.Use (a + b)² = a² + 2ab + b² to find 89².
34. 34.If a + b = 4 and ab = 3, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 84 × 76.
36. 36.Use (a + b)² = a² + 2ab + b² to find 17².
37. 37.Use a² − b² = (a + b)(a − b) to find 60² − 39².
38. 38.If a − b = 1 and ab = 2, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 90² − 51².
40. 40.If a − b = 2 and ab = 3, what is a² + b²?

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