Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 625 · 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 71².
2. 2.Find the value of x² + 2xy + y² when x = 15 and y = 1.
3. 3.If a + b = 5 and ab = 4, what is a² + b²?
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 94².
6. 6.Use a² − b² = (a + b)(a − b) to find 30² − 5².
7. 7.Use (a + b)² = a² + 2ab + b² to find 91².
8. 8.Use (a + b)² = a² + 2ab + b² to find 53².
9. 9.Use (a + b)² = a² + 2ab + b² to find 25².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Use (a + b)² = a² + 2ab + b² to find 71².
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 3.
13. 13.Find the value of x² + 2xy + y² when x = 7 and y = 3.
14. 14.Use a² − b² = (a + b)(a − b) to find 59² − 1².
15. 15.Use (a + b)² = a² + 2ab + b² to find 69².
16. 16.Use (a + b)² = a² + 2ab + b² to find 88².
17. 17.Use (a + b)² = a² + 2ab + b² to find 49².
18. 18.Use a² − b² = (a + b)(a − b) to find 87² − 51².
19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 8.
20. 20.Use a² − b² = (a + b)(a − b) to find 63² − 56².
21. 21.Use (a + b)(a − b) = a² − b² to find 21 × 19.
22. 22.Use (a − b)² = a² − 2ab + b² to find 77².
23. 23.Use (a + b)(a − b) = a² − b² to find 81 × 79.
24. 24.Use a² − b² = (a + b)(a − b) to find 70² − 14².
25. 25.Use (a + b)² = a² + 2ab + b² to find 61².
26. 26.If a − b = 1 and ab = 2, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 33² − 21².
28. 28.Use (a + b)(a − b) = a² − b² to find 87 × 73.
29. 29.Use (a − b)² = a² − 2ab + b² to find 99².
30. 30.If a + b = 6 and ab = 5, what is a² + b²?
31. 31.If a + b = 10 and ab = 9, what is a² + b²?
32. 32.If a + b = 13 and ab = 22, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 14 and y = 7.
34. 34.Use (a − b)² = a² − 2ab + b² to find 87².
35. 35.Use (a + b)² = a² + 2ab + b² to find 24².
36. 36.Use (a − b)² = a² − 2ab + b² to find 91².
37. 37.Use a² − b² = (a + b)(a − b) to find 40² − 8².
38. 38.Find the value of x² − 2xy + y² when x = 10 and y = 9.
39. 39.Use (a + b)(a − b) = a² − b² to find 56 × 44.
40. 40.Use (a − b)² = a² − 2ab + b² to find 68².

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