Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 488 · 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 43 × 37.
2. 2.Use (a + b)(a − b) = a² − b² to find 65 × 55.
3. 3.If a − b = 7 and ab = 18, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 93 × 87.
5. 5.Use (a + b)(a − b) = a² − b² to find 79 × 61.
6. 6.Use (a − b)² = a² − 2ab + b² to find 26².
7. 7.Use a² − b² = (a + b)(a − b) to find 36² − 8².
8. 8.If a + b = 19 and ab = 88, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 4 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 98².
11. 11.Use (a + b)(a − b) = a² − b² to find 35 × 25.
12. 12.Find the value of x² − y² when x = 7 and y = 6.
13. 13.Use (a + b)² = a² + 2ab + b² to find 96².
14. 14.Use (a + b)² = a² + 2ab + b² to find 27².
15. 15.Use (a + b)² = a² + 2ab + b² to find 16².
16. 16.Use (a − b)² = a² − 2ab + b² to find 14².
17. 17.Find the value of x² − 2xy + y² when x = 7 and y = 4.
18. 18.Use (a − b)² = a² − 2ab + b² to find 15².
19. 19.If a − b = 6 and ab = 16, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 24² − 23².
21. 21.Use (a + b)(a − b) = a² − b² to find 26 × 14.
22. 22.Use (a − b)² = a² − 2ab + b² to find 59².
23. 23.Find the value of x² − 2xy + y² when x = 9 and y = 6.
24. 24.Find the value of x² + 2xy + y² when x = 13 and y = 12.
25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 12.
26. 26.Use a² − b² = (a + b)(a − b) to find 57² − 49².
27. 27.Find the value of x² − 2xy + y² when x = 15 and y = 1.
28. 28.If a − b = 2 and ab = 8, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 24² − 12².
30. 30.Find the value of x² + 2xy + y² when x = 6 and y = 3.
31. 31.Use (a + b)² = a² + 2ab + b² to find 98².
32. 32.If a − b = 9 and ab = 36, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 32 × 28.
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.If a + b = 20 and ab = 96, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 41 × 39.
37. 37.Use (a − b)² = a² − 2ab + b² to find 93².
38. 38.Find the value of x² + 2xy + y² when x = 5 and y = 1.
39. 39.Find the value of x² + 2xy + y² when x = 9 and y = 6.
40. 40.Use a² − b² = (a + b)(a − b) to find 73² − 61².

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