Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 737 · 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 68².
2. 2.Use a² − b² = (a + b)(a − b) to find 89² − 38².
3. 3.Use a² − b² = (a + b)(a − b) to find 84² − 80².
4. 4.Use (a + b)² = a² + 2ab + b² to find 77².
5. 5.Find the value of x² − 2xy + y² when x = 15 and y = 12.
6. 6.Use (a − b)² = a² − 2ab + b² to find 61².
7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 2.
8. 8.Use a² − b² = (a + b)(a − b) to find 93² − 39².
9. 9.Use a² − b² = (a + b)(a − b) to find 41² − 15².
10. 10.If a + b = 5 and ab = 4, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 32 × 28.
12. 12.Find the value of x² − 2xy + y² when x = 12 and y = 7.
13. 13.Use (a + b)(a − b) = a² − b² to find 24 × 16.
14. 14.Use (a + b)(a − b) = a² − b² to find 53 × 47.
15. 15.Find the value of x² − y² when x = 6 and y = 4.
16. 16.Use (a + b)² = a² + 2ab + b² to find 16².
17. 17.If a + b = 10 and ab = 21, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 53².
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.If a + b = 16 and ab = 48, what is a² + b²?
21. 21.If a + b = 13 and ab = 42, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 74².
23. 23.Use (a + b)(a − b) = a² − b² to find 46 × 34.
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 1.
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 62 × 58.
27. 27.Use a² − b² = (a + b)(a − b) to find 42² − 40².
28. 28.Use (a + b)(a − b) = a² − b² to find 77 × 63.
29. 29.Use (a + b)² = a² + 2ab + b² to find 67².
30. 30.Use a² − b² = (a + b)(a − b) to find 21² − 12².
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.Find the value of x² + 2xy + y² when x = 13 and y = 3.
33. 33.Use a² − b² = (a + b)(a − b) to find 27² − 5².
34. 34.Use a² − b² = (a + b)(a − b) to find 99² − 67².
35. 35.Use a² − b² = (a + b)(a − b) to find 53² − 26².
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 22² − 4².
38. 38.Use (a − b)² = a² − 2ab + b² to find 49².
39. 39.Use (a + b)² = a² + 2ab + b² to find 63².
40. 40.Use (a + b)² = a² + 2ab + b² to find 104².

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