Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 602 · 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.Find the value of x² − 2xy + y² when x = 13 and y = 9.
2. 2.Use (a + b)² = a² + 2ab + b² to find 35².
3. 3.Use a² − b² = (a + b)(a − b) to find 70² − 52².
4. 4.Use (a + b)² = a² + 2ab + b² to find 104².
5. 5.If a + b = 16 and ab = 63, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 73².
7. 7.Use (a + b)² = a² + 2ab + b² to find 24².
8. 8.If a − b = 10 and ab = 11, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 87² − 1².
10. 10.If a − b = 1 and ab = 12, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 38² − 23².
12. 12.Use (a + b)(a − b) = a² − b² to find 49 × 31.
13. 13.Use (a + b)² = a² + 2ab + b² to find 45².
14. 14.Use (a + b)(a − b) = a² − b² to find 53 × 47.
15. 15.Use a² − b² = (a + b)(a − b) to find 83² − 62².
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.Use (a + b)² = a² + 2ab + b² to find 21².
18. 18.Use (a − b)² = a² − 2ab + b² to find 95².
19. 19.Use (a − b)² = a² − 2ab + b² to find 77².
20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
21. 21.Use a² − b² = (a + b)(a − b) to find 54² − 42².
22. 22.Use (a + b)² = a² + 2ab + b² to find 34².
23. 23.Use a² − b² = (a + b)(a − b) to find 41² − 20².
24. 24.Use (a + b)² = a² + 2ab + b² to find 56².
25. 25.Use a² − b² = (a + b)(a − b) to find 24² − 1².
26. 26.Use (a + b)(a − b) = a² − b² to find 67 × 53.
27. 27.If a + b = 16 and ab = 60, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 64².
29. 29.Use (a + b)(a − b) = a² − b² to find 62 × 58.
30. 30.Find the value of x² + 2xy + y² when x = 13 and y = 4.
31. 31.Use (a + b)(a − b) = a² − b² to find 101 × 99.
32. 32.Use (a + b)² = a² + 2ab + b² to find 39².
33. 33.Use a² − b² = (a + b)(a − b) to find 84² − 44².
34. 34.If a − b = 4 and ab = 60, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 6.
36. 36.Use a² − b² = (a + b)(a − b) to find 61² − 24².
37. 37.Use (a − b)² = a² − 2ab + b² to find 98².
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 3.
39. 39.Use (a − b)² = a² − 2ab + b² to find 44².
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 1.

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