Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 404 · 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 38².
2. 2.Use a² − b² = (a + b)(a − b) to find 52² − 7².
3. 3.Use (a − b)² = a² − 2ab + b² to find 64².
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.If a − b = 9 and ab = 10, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 42² − 18².
7. 7.Use (a − b)² = a² − 2ab + b² to find 16².
8. 8.Use (a + b)² = a² + 2ab + b² to find 36².
9. 9.Use (a − b)² = a² − 2ab + b² to find 97².
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 7.
11. 11.Use (a + b)² = a² + 2ab + b² to find 44².
12. 12.Use (a + b)(a − b) = a² − b² to find 72 × 68.
13. 13.Find the value of x² − y² when x = 3 and y = 2.
14. 14.If a + b = 9 and ab = 14, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 61².
16. 16.Use a² − b² = (a + b)(a − b) to find 27² − 8².
17. 17.Use (a − b)² = a² − 2ab + b² to find 99².
18. 18.Use (a + b)² = a² + 2ab + b² to find 87².
19. 19.Use (a + b)² = a² + 2ab + b² to find 32².
20. 20.Use (a + b)² = a² + 2ab + b² to find 16².
21. 21.Find the value of x² − 2xy + y² when x = 5 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 68².
23. 23.Use (a − b)² = a² − 2ab + b² to find 12².
24. 24.Use (a + b)(a − b) = a² − b² to find 91 × 89.
25. 25.Use (a + b)² = a² + 2ab + b² to find 58².
26. 26.Find the value of x² − 2xy + y² when x = 9 and y = 3.
27. 27.Use (a − b)² = a² − 2ab + b² to find 56².
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 26 × 14.
30. 30.Use a² − b² = (a + b)(a − b) to find 46² − 10².
31. 31.Use a² − b² = (a + b)(a − b) to find 35² − 32².
32. 32.Use (a + b)(a − b) = a² − b² to find 34 × 26.
33. 33.Use (a + b)(a − b) = a² − b² to find 23 × 17.
34. 34.Use (a − b)² = a² − 2ab + b² to find 75².
35. 35.Use a² − b² = (a + b)(a − b) to find 30² − 8².
36. 36.Find the value of x² − y² when x = 7 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 81² − 4².
38. 38.Use a² − b² = (a + b)(a − b) to find 76² − 70².
39. 39.Find the value of x² + 2xy + y² when x = 12 and y = 7.
40. 40.If a − b = 7 and ab = 18, what is a² + b²?

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