Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 132 · 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 49².
2. 2.Use a² − b² = (a + b)(a − b) to find 86² − 6².
3. 3.Use (a + b)(a − b) = a² − b² to find 61 × 59.
4. 4.Use (a + b)(a − b) = a² − b² to find 64 × 56.
5. 5.Use (a − b)² = a² − 2ab + b² to find 34².
6. 6.Find the value of x² − y² when x = 5 and y = 1.
7. 7.Use (a − b)² = a² − 2ab + b² to find 24².
8. 8.Use (a − b)² = a² − 2ab + b² to find 62².
9. 9.Find the value of x² − y² when x = 12 and y = 7.
10. 10.Find the value of x² − y² when x = 6 and y = 5.
11. 11.Use (a + b)² = a² + 2ab + b² to find 34².
12. 12.Find the value of x² − y² when x = 4 and y = 2.
13. 13.Use (a + b)² = a² + 2ab + b² to find 66².
14. 14.Find the value of x² − y² when x = 9 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 74².
16. 16.Use (a + b)² = a² + 2ab + b² to find 41².
17. 17.Use (a + b)² = a² + 2ab + b² to find 32².
18. 18.Use (a + b)(a − b) = a² − b² to find 72 × 68.
19. 19.If a + b = 12 and ab = 35, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 69².
21. 21.Use (a + b)(a − b) = a² − b² to find 93 × 87.
22. 22.Use (a + b)(a − b) = a² − b² to find 65 × 55.
23. 23.Use (a + b)² = a² + 2ab + b² to find 25².
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Use (a + b)² = a² + 2ab + b² to find 12².
26. 26.Find the value of x² − y² when x = 8 and y = 2.
27. 27.Use a² − b² = (a + b)(a − b) to find 93² − 21².
28. 28.Use (a + b)² = a² + 2ab + b² to find 76².
29. 29.Find the value of x² + 2xy + y² when x = 10 and y = 7.
30. 30.Use (a + b)² = a² + 2ab + b² to find 53².
31. 31.Find the value of x² + 2xy + y² when x = 8 and y = 2.
32. 32.If a − b = 1 and ab = 90, what is a² + b²?
33. 33.If a − b = 1 and ab = 12, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 1.
35. 35.Use (a + b)(a − b) = a² − b² to find 96 × 84.
36. 36.Use (a − b)² = a² − 2ab + b² to find 19².
37. 37.Use a² − b² = (a + b)(a − b) to find 85² − 46².
38. 38.Use (a + b)(a − b) = a² − b² to find 31 × 29.
39. 39.Use (a + b)(a − b) = a² − b² to find 91 × 89.
40. 40.Use a² − b² = (a + b)(a − b) to find 31² − 24².

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