Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 36 · 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 104 × 96.
2. 2.Use (a + b)(a − b) = a² − b² to find 79 × 61.
3. 3.Use (a + b)(a − b) = a² − b² to find 27 × 13.
4. 4.Use (a + b)² = a² + 2ab + b² to find 26².
5. 5.Use a² − b² = (a + b)(a − b) to find 85² − 25².
6. 6.Use a² − b² = (a + b)(a − b) to find 61² − 11².
7. 7.If a + b = 7 and ab = 12, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 28².
9. 9.If a + b = 15 and ab = 56, what is a² + b²?
10. 10.If a − b = 2 and ab = 24, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 59².
12. 12.Use (a + b)² = a² + 2ab + b² to find 13².
13. 13.Use a² − b² = (a + b)(a − b) to find 49² − 32².
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 12.
15. 15.If a + b = 13 and ab = 36, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 32².
17. 17.Use a² − b² = (a + b)(a − b) to find 73² − 44².
18. 18.Find the value of x² − y² when x = 12 and y = 11.
19. 19.Use (a − b)² = a² − 2ab + b² to find 75².
20. 20.Use (a + b)(a − b) = a² − b² to find 21 × 19.
21. 21.Use (a + b)² = a² + 2ab + b² to find 67².
22. 22.Find the value of x² − 2xy + y² when x = 12 and y = 4.
23. 23.Find the value of x² − 2xy + y² when x = 4 and y = 1.
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 3.
25. 25.Use (a + b)(a − b) = a² − b² to find 38 × 22.
26. 26.If a + b = 11 and ab = 28, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 11 and y = 1.
28. 28.Use (a − b)² = a² − 2ab + b² to find 85².
29. 29.If a + b = 6 and ab = 8, what is a² + b²?
30. 30.If a − b = 7 and ab = 30, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.Use (a + b)(a − b) = a² − b² to find 83 × 77.
33. 33.Use (a + b)(a − b) = a² − b² to find 48 × 32.
34. 34.Find the value of x² − y² when x = 4 and y = 2.
35. 35.Use a² − b² = (a + b)(a − b) to find 99² − 55².
36. 36.Use (a − b)² = a² − 2ab + b² to find 63².
37. 37.Use (a − b)² = a² − 2ab + b² to find 48².
38. 38.Find the value of x² + 2xy + y² when x = 14 and y = 6.
39. 39.If a − b = 1 and ab = 6, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 12 and y = 11.

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