Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 270 · 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 a² − b² = (a + b)(a − b) to find 44² − 7².
2. 2.If a − b = 3 and ab = 28, what is a² + b²?
3. 3.If a + b = 4 and ab = 3, what is a² + b²?
4. 4.If a + b = 13 and ab = 40, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.Use a² − b² = (a + b)(a − b) to find 67² − 24².
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 49².
9. 9.Use (a + b)(a − b) = a² − b² to find 46 × 34.
10. 10.Use (a + b)(a − b) = a² − b² to find 31 × 29.
11. 11.Use a² − b² = (a + b)(a − b) to find 57² − 53².
12. 12.If a − b = 4 and ab = 21, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 68² − 4².
14. 14.Use a² − b² = (a + b)(a − b) to find 33² − 20².
15. 15.Use a² − b² = (a + b)(a − b) to find 87² − 60².
16. 16.Use a² − b² = (a + b)(a − b) to find 89² − 5².
17. 17.Use a² − b² = (a + b)(a − b) to find 89² − 36².
18. 18.Use (a + b)(a − b) = a² − b² to find 21 × 19.
19. 19.Use (a + b)(a − b) = a² − b² to find 108 × 92.
20. 20.Use (a − b)² = a² − 2ab + b² to find 65².
21. 21.Find the value of x² − 2xy + y² when x = 6 and y = 5.
22. 22.Use (a − b)² = a² − 2ab + b² to find 53².
23. 23.Use (a + b)² = a² + 2ab + b² to find 84².
24. 24.Use (a − b)² = a² − 2ab + b² to find 37².
25. 25.Use (a + b)(a − b) = a² − b² to find 27 × 13.
26. 26.If a + b = 5 and ab = 4, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 4.
28. 28.Use (a − b)² = a² − 2ab + b² to find 99².
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.Use (a − b)² = a² − 2ab + b² to find 29².
31. 31.Find the value of x² − y² when x = 5 and y = 2.
32. 32.Find the value of x² + 2xy + y² when x = 12 and y = 9.
33. 33.Use (a + b)² = a² + 2ab + b² to find 12².
34. 34.Find the value of x² − 2xy + y² when x = 8 and y = 7.
35. 35.Use (a − b)² = a² − 2ab + b² to find 28².
36. 36.Use (a + b)(a − b) = a² − b² to find 42 × 38.
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 82² − 51².
39. 39.Use (a − b)² = a² − 2ab + b² to find 86².
40. 40.Use a² − b² = (a + b)(a − b) to find 81² − 1².

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