Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 280 · 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 46².
2. 2.Use (a + b)² = a² + 2ab + b² to find 16².
3. 3.Find the value of x² + 2xy + y² when x = 12 and y = 5.
4. 4.Use (a + b)(a − b) = a² − b² to find 77 × 63.
5. 5.Find the value of x² − y² when x = 13 and y = 4.
6. 6.Use (a − b)² = a² − 2ab + b² to find 54².
7. 7.Use (a + b)² = a² + 2ab + b² to find 38².
8. 8.Use a² − b² = (a + b)(a − b) to find 70² − 38².
9. 9.Use (a + b)² = a² + 2ab + b² to find 65².
10. 10.Use a² − b² = (a + b)(a − b) to find 60² − 15².
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 27² − 6².
13. 13.Use (a + b)(a − b) = a² − b² to find 65 × 55.
14. 14.Use (a − b)² = a² − 2ab + b² to find 87².
15. 15.Use (a − b)² = a² − 2ab + b² to find 57².
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.Use (a + b)(a − b) = a² − b² to find 64 × 56.
18. 18.Use (a − b)² = a² − 2ab + b² to find 21².
19. 19.Use (a − b)² = a² − 2ab + b² to find 79².
20. 20.Use (a − b)² = a² − 2ab + b² to find 11².
21. 21.Use (a − b)² = a² − 2ab + b² to find 78².
22. 22.Use a² − b² = (a + b)(a − b) to find 37² − 23².
23. 23.Use (a − b)² = a² − 2ab + b² to find 19².
24. 24.Use (a + b)² = a² + 2ab + b² to find 101².
25. 25.Use a² − b² = (a + b)(a − b) to find 29² − 1².
26. 26.Use (a − b)² = a² − 2ab + b² to find 69².
27. 27.Use (a − b)² = a² − 2ab + b² to find 47².
28. 28.If a + b = 13 and ab = 40, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 37² − 15².
30. 30.Use (a − b)² = a² − 2ab + b² to find 24².
31. 31.Find the value of x² + 2xy + y² when x = 15 and y = 13.
32. 32.Use (a − b)² = a² − 2ab + b² to find 97².
33. 33.Use (a + b)² = a² + 2ab + b² to find 44².
34. 34.Use (a + b)(a − b) = a² − b² to find 106 × 94.
35. 35.If a + b = 9 and ab = 18, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 32 × 28.
37. 37.Use (a − b)² = a² − 2ab + b² to find 32².
38. 38.Use (a + b)(a − b) = a² − b² to find 46 × 34.
39. 39.Find the value of x² − 2xy + y² when x = 3 and y = 2.
40. 40.Find the value of x² − 2xy + y² when x = 11 and y = 9.

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