Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 137 · 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 a² − b² = (a + b)(a − b) to find 30² − 9².
2. 2.Use (a + b)(a − b) = a² − b² to find 78 × 62.
3. 3.Use a² − b² = (a + b)(a − b) to find 47² − 21².
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 79² − 72².
6. 6.If a − b = 4 and ab = 21, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 26² − 4².
8. 8.Use (a + b)² = a² + 2ab + b² to find 57².
9. 9.Use (a + b)² = a² + 2ab + b² to find 45².
10. 10.Use (a − b)² = a² − 2ab + b² to find 82².
11. 11.Find the value of x² + 2xy + y² when x = 7 and y = 4.
12. 12.Use (a − b)² = a² − 2ab + b² to find 49².
13. 13.Find the value of x² + 2xy + y² when x = 6 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 25².
15. 15.Use (a − b)² = a² − 2ab + b² to find 24².
16. 16.If a − b = 10 and ab = 11, what is a² + b²?
17. 17.If a + b = 8 and ab = 15, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 6 and y = 2.
19. 19.Use (a + b)² = a² + 2ab + b² to find 25².
20. 20.Use a² − b² = (a + b)(a − b) to find 32² − 2².
21. 21.Find the value of x² − 2xy + y² when x = 12 and y = 1.
22. 22.Use (a + b)(a − b) = a² − b² to find 62 × 58.
23. 23.Use (a + b)(a − b) = a² − b² to find 28 × 12.
24. 24.Find the value of x² − y² when x = 7 and y = 3.
25. 25.If a − b = 1 and ab = 12, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 72².
27. 27.Use a² − b² = (a + b)(a − b) to find 60² − 44².
28. 28.Use (a + b)(a − b) = a² − b² to find 43 × 37.
29. 29.Use (a − b)² = a² − 2ab + b² to find 56².
30. 30.If a − b = 2 and ab = 3, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 7.
32. 32.Use (a + b)(a − b) = a² − b² to find 67 × 53.
33. 33.If a − b = 1 and ab = 2, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 35².
35. 35.Find the value of x² − 2xy + y² when x = 15 and y = 3.
36. 36.Use (a + b)² = a² + 2ab + b² to find 109².
37. 37.Use (a + b)² = a² + 2ab + b² to find 16².
38. 38.Use (a + b)² = a² + 2ab + b² to find 28².
39. 39.Use (a − b)² = a² − 2ab + b² to find 37².
40. 40.Use a² − b² = (a + b)(a − b) to find 69² − 58².

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