Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 426 · 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 = 14 and y = 11.
2. 2.If a + b = 16 and ab = 48, what is a² + b²?
3. 3.If a + b = 5 and ab = 6, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 61².
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Use (a + b)(a − b) = a² − b² to find 85 × 75.
7. 7.Find the value of x² + 2xy + y² when x = 14 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 92 × 88.
9. 9.Use (a − b)² = a² − 2ab + b² to find 27².
10. 10.Use a² − b² = (a + b)(a − b) to find 23² − 13².
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Use (a + b)² = a² + 2ab + b² to find 62².
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 1.
14. 14.Use (a + b)² = a² + 2ab + b² to find 37².
15. 15.Use (a − b)² = a² − 2ab + b² to find 47².
16. 16.Use (a + b)(a − b) = a² − b² to find 96 × 84.
17. 17.Use a² − b² = (a + b)(a − b) to find 92² − 73².
18. 18.Find the value of x² − y² when x = 9 and y = 5.
19. 19.Use (a + b)(a − b) = a² − b² to find 89 × 71.
20. 20.Use (a + b)(a − b) = a² − b² to find 104 × 96.
21. 21.Use (a − b)² = a² − 2ab + b² to find 13².
22. 22.Use (a + b)² = a² + 2ab + b² to find 26².
23. 23.Use a² − b² = (a + b)(a − b) to find 86² − 49².
24. 24.Find the value of x² + 2xy + y² when x = 14 and y = 7.
25. 25.Use a² − b² = (a + b)(a − b) to find 74² − 3².
26. 26.Use (a − b)² = a² − 2ab + b² to find 26².
27. 27.Use (a + b)² = a² + 2ab + b² to find 83².
28. 28.Use (a − b)² = a² − 2ab + b² to find 84².
29. 29.Use a² − b² = (a + b)(a − b) to find 21² − 18².
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 4.
31. 31.Use (a + b)(a − b) = a² − b² to find 37 × 23.
32. 32.Use (a − b)² = a² − 2ab + b² to find 73².
33. 33.Use (a − b)² = a² − 2ab + b² to find 67².
34. 34.Use (a + b)² = a² + 2ab + b² to find 18².
35. 35.Use (a − b)² = a² − 2ab + b² to find 57².
36. 36.Use a² − b² = (a + b)(a − b) to find 24² − 12².
37. 37.Use (a + b)(a − b) = a² − b² to find 77 × 63.
38. 38.Use (a + b)² = a² + 2ab + b² to find 13².
39. 39.If a − b = 3 and ab = 40, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 51² − 13².

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