Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 129 · 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 = 3 and y = 2.
2. 2.If a + b = 12 and ab = 35, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 66².
4. 4.Use (a + b)² = a² + 2ab + b² to find 56².
5. 5.Use a² − b² = (a + b)(a − b) to find 91² − 3².
6. 6.Use a² − b² = (a + b)(a − b) to find 92² − 12².
7. 7.Use (a + b)² = a² + 2ab + b² to find 97².
8. 8.If a − b = 2 and ab = 15, what is a² + b²?
9. 9.Find the value of x² − y² when x = 15 and y = 6.
10. 10.Use (a + b)(a − b) = a² − b² to find 94 × 86.
11. 11.Find the value of x² − 2xy + y² when x = 12 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 47 × 33.
13. 13.Use (a − b)² = a² − 2ab + b² to find 81².
14. 14.Use (a − b)² = a² − 2ab + b² to find 86².
15. 15.Use (a + b)² = a² + 2ab + b² to find 86².
16. 16.Use (a − b)² = a² − 2ab + b² to find 67².
17. 17.Use (a + b)² = a² + 2ab + b² to find 79².
18. 18.If a + b = 7 and ab = 12, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 6 and y = 4.
20. 20.Use (a − b)² = a² − 2ab + b² to find 33².
21. 21.If a − b = 5 and ab = 36, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 43².
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 1².
24. 24.Use a² − b² = (a + b)(a − b) to find 83² − 44².
25. 25.Use (a + b)² = a² + 2ab + b² to find 57².
26. 26.If a − b = 5 and ab = 14, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 20² − 12².
28. 28.Use a² − b² = (a + b)(a − b) to find 98² − 56².
29. 29.Find the value of x² − y² when x = 6 and y = 5.
30. 30.Use (a + b)(a − b) = a² − b² to find 68 × 52.
31. 31.Use (a + b)(a − b) = a² − b² to find 97 × 83.
32. 32.Use (a + b)² = a² + 2ab + b² to find 104².
33. 33.Use (a − b)² = a² − 2ab + b² to find 39².
34. 34.Find the value of x² − y² when x = 9 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 41².
36. 36.Find the value of x² − y² when x = 15 and y = 13.
37. 37.Use (a + b)² = a² + 2ab + b² to find 66².
38. 38.If a + b = 4 and ab = 3, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 35².
40. 40.Use (a − b)² = a² − 2ab + b² to find 34².

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