Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 797 · 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 48² − 9².
2. 2.Use (a + b)² = a² + 2ab + b² to find 91².
3. 3.Use a² − b² = (a + b)(a − b) to find 25² − 10².
4. 4.Use (a − b)² = a² − 2ab + b² to find 33².
5. 5.Use (a + b)² = a² + 2ab + b² to find 93².
6. 6.Use (a − b)² = a² − 2ab + b² to find 42².
7. 7.Use (a + b)(a − b) = a² − b² to find 38 × 22.
8. 8.Use (a − b)² = a² − 2ab + b² to find 89².
9. 9.Use (a + b)(a − b) = a² − b² to find 62 × 58.
10. 10.If a + b = 13 and ab = 42, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 43² − 26².
12. 12.Find the value of x² − 2xy + y² when x = 4 and y = 3.
13. 13.Use (a + b)(a − b) = a² − b² to find 48 × 32.
14. 14.Use (a + b)² = a² + 2ab + b² to find 62².
15. 15.Find the value of x² − y² when x = 15 and y = 12.
16. 16.Use (a − b)² = a² − 2ab + b² to find 17².
17. 17.Use (a − b)² = a² − 2ab + b² to find 12².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 9.
19. 19.Find the value of x² + 2xy + y² when x = 11 and y = 7.
20. 20.If a − b = 2 and ab = 3, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use a² − b² = (a + b)(a − b) to find 54² − 51².
23. 23.Use (a + b)² = a² + 2ab + b² to find 24².
24. 24.Use a² − b² = (a + b)(a − b) to find 33² − 32².
25. 25.If a − b = 1 and ab = 6, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 41².
27. 27.Use (a + b)² = a² + 2ab + b² to find 85².
28. 28.Use (a − b)² = a² − 2ab + b² to find 64².
29. 29.Use a² − b² = (a + b)(a − b) to find 79² − 9².
30. 30.Use (a + b)(a − b) = a² − b² to find 88 × 72.
31. 31.Use (a + b)(a − b) = a² − b² to find 58 × 42.
32. 32.Use (a + b)(a − b) = a² − b² to find 98 × 82.
33. 33.Use (a + b)² = a² + 2ab + b² to find 16².
34. 34.Find the value of x² − 2xy + y² when x = 7 and y = 1.
35. 35.Find the value of x² − 2xy + y² when x = 9 and y = 8.
36. 36.Use a² − b² = (a + b)(a − b) to find 51² − 23².
37. 37.Find the value of x² − y² when x = 13 and y = 4.
38. 38.Use a² − b² = (a + b)(a − b) to find 87² − 20².
39. 39.Find the value of x² − y² when x = 6 and y = 2.
40. 40.If a + b = 12 and ab = 32, what is a² + b²?

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