Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 75 · 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 a² − b² = (a + b)(a − b) to find 36² − 22².
2. 2.Find the value of x² − 2xy + y² when x = 7 and y = 4.
3. 3.Use (a + b)(a − b) = a² − b² to find 52 × 48.
4. 4.Find the value of x² + 2xy + y² when x = 4 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 88².
6. 6.Use a² − b² = (a + b)(a − b) to find 20² − 4².
7. 7.Use a² − b² = (a + b)(a − b) to find 52² − 24².
8. 8.Use (a − b)² = a² − 2ab + b² to find 79².
9. 9.Find the value of x² + 2xy + y² when x = 8 and y = 7.
10. 10.Use (a + b)² = a² + 2ab + b² to find 78².
11. 11.Find the value of x² + 2xy + y² when x = 9 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 84² − 19².
13. 13.Use (a − b)² = a² − 2ab + b² to find 46².
14. 14.Use (a + b)² = a² + 2ab + b² to find 29².
15. 15.Find the value of x² − 2xy + y² when x = 9 and y = 4.
16. 16.Use (a + b)(a − b) = a² − b² to find 99 × 81.
17. 17.Find the value of x² − y² when x = 7 and y = 5.
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use (a + b)(a − b) = a² − b² to find 101 × 99.
20. 20.Use (a + b)² = a² + 2ab + b² to find 73².
21. 21.Use (a − b)² = a² − 2ab + b² to find 94².
22. 22.Find the value of x² − y² when x = 6 and y = 2.
23. 23.Use (a + b)² = a² + 2ab + b² to find 27².
24. 24.Use (a + b)² = a² + 2ab + b² to find 106².
25. 25.If a − b = 3 and ab = 4, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 59 × 41.
27. 27.Use (a + b)(a − b) = a² − b² to find 106 × 94.
28. 28.Use (a + b)(a − b) = a² − b² to find 43 × 37.
29. 29.Find the value of x² + 2xy + y² when x = 5 and y = 2.
30. 30.Find the value of x² + 2xy + y² when x = 4 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 99².
32. 32.If a − b = 1 and ab = 6, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 6 and y = 2.
34. 34.If a − b = 8 and ab = 33, what is a² + b²?
35. 35.Find the value of x² − y² when x = 3 and y = 2.
36. 36.Use (a − b)² = a² − 2ab + b² to find 48².
37. 37.Use (a + b)² = a² + 2ab + b² to find 81².
38. 38.Find the value of x² + 2xy + y² when x = 13 and y = 8.
39. 39.Use (a + b)² = a² + 2ab + b² to find 85².
40. 40.Use (a − b)² = a² − 2ab + b² to find 11².

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