Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 140 · 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)² = a² + 2ab + b² to find 98².
2. 2.Find the value of x² − y² when x = 10 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 14².
4. 4.If a + b = 8 and ab = 7, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 13².
6. 6.Use a² − b² = (a + b)(a − b) to find 35² − 7².
7. 7.Use (a − b)² = a² − 2ab + b² to find 79².
8. 8.Use a² − b² = (a + b)(a − b) to find 37² − 26².
9. 9.Find the value of x² + 2xy + y² when x = 3 and y = 2.
10. 10.If a + b = 11 and ab = 28, what is a² + b²?
11. 11.If a − b = 5 and ab = 50, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 104 × 96.
13. 13.Use (a + b)² = a² + 2ab + b² to find 56².
14. 14.Use (a + b)² = a² + 2ab + b² to find 34².
15. 15.Use a² − b² = (a + b)(a − b) to find 37² − 10².
16. 16.Use (a − b)² = a² − 2ab + b² to find 41².
17. 17.If a + b = 4 and ab = 3, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 88².
19. 19.Use (a − b)² = a² − 2ab + b² to find 89².
20. 20.Use (a + b)(a − b) = a² − b² to find 87 × 73.
21. 21.Use (a + b)(a − b) = a² − b² to find 33 × 27.
22. 22.Use (a + b)² = a² + 2ab + b² to find 19².
23. 23.Use a² − b² = (a + b)(a − b) to find 78² − 42².
24. 24.Use (a − b)² = a² − 2ab + b² to find 71².
25. 25.Find the value of x² + 2xy + y² when x = 5 and y = 4.
26. 26.Use a² − b² = (a + b)(a − b) to find 49² − 4².
27. 27.If a − b = 6 and ab = 7, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 24² − 8².
29. 29.Find the value of x² + 2xy + y² when x = 9 and y = 7.
30. 30.Find the value of x² − 2xy + y² when x = 12 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 51².
32. 32.Use (a + b)(a − b) = a² − b² to find 34 × 26.
33. 33.Use a² − b² = (a + b)(a − b) to find 82² − 24².
34. 34.Use (a + b)(a − b) = a² − b² to find 36 × 24.
35. 35.If a − b = 3 and ab = 70, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 63².
37. 37.Use (a + b)² = a² + 2ab + b² to find 71².
38. 38.Use a² − b² = (a + b)(a − b) to find 28² − 26².
39. 39.Find the value of x² + 2xy + y² when x = 12 and y = 6.
40. 40.Find the value of x² + 2xy + y² when x = 12 and y = 9.

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