Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 50 · 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 = 15 and y = 11.
2. 2.Use (a − b)² = a² − 2ab + b² to find 65².
3. 3.Use (a − b)² = a² − 2ab + b² to find 97².
4. 4.If a − b = 2 and ab = 48, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 33 × 27.
6. 6.Use (a + b)(a − b) = a² − b² to find 102 × 98.
7. 7.Find the value of x² + 2xy + y² when x = 8 and y = 1.
8. 8.Use (a − b)² = a² − 2ab + b² to find 15².
9. 9.Use (a − b)² = a² − 2ab + b² to find 94².
10. 10.Use (a + b)² = a² + 2ab + b² to find 27².
11. 11.Use a² − b² = (a + b)(a − b) to find 77² − 21².
12. 12.Use (a − b)² = a² − 2ab + b² to find 81².
13. 13.Use (a − b)² = a² − 2ab + b² to find 64².
14. 14.Use a² − b² = (a + b)(a − b) to find 74² − 57².
15. 15.Use a² − b² = (a + b)(a − b) to find 23² − 17².
16. 16.Use (a + b)² = a² + 2ab + b² to find 12².
17. 17.Use (a − b)² = a² − 2ab + b² to find 98².
18. 18.Use a² − b² = (a + b)(a − b) to find 48² − 36².
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 5.
20. 20.Use (a + b)(a − b) = a² − b² to find 98 × 82.
21. 21.Use (a + b)(a − b) = a² − b² to find 85 × 75.
22. 22.Use a² − b² = (a + b)(a − b) to find 52² − 1².
23. 23.If a + b = 3 and ab = 2, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 89².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Use (a − b)² = a² − 2ab + b² to find 92².
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Use a² − b² = (a + b)(a − b) to find 41² − 15².
31. 31.Use (a + b)² = a² + 2ab + b² to find 22².
32. 32.Use (a + b)² = a² + 2ab + b² to find 58².
33. 33.Use a² − b² = (a + b)(a − b) to find 55² − 42².
34. 34.If a − b = 6 and ab = 7, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 84² − 49².
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 4.
37. 37.Use (a + b)² = a² + 2ab + b² to find 38².
38. 38.Use (a + b)(a − b) = a² − b² to find 86 × 74.
39. 39.Use (a + b)² = a² + 2ab + b² to find 104².
40. 40.Use (a − b)² = a² − 2ab + b² to find 49².

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