Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 491 · 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 = 12 and y = 11.
2. 2.Use (a − b)² = a² − 2ab + b² to find 98².
3. 3.If a + b = 8 and ab = 12, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 99².
5. 5.Use (a + b)² = a² + 2ab + b² to find 95².
6. 6.Use a² − b² = (a + b)(a − b) to find 37² − 21².
7. 7.If a + b = 17 and ab = 70, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 81².
9. 9.If a − b = 1 and ab = 6, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 104².
11. 11.Use (a + b)(a − b) = a² − b² to find 39 × 21.
12. 12.Use a² − b² = (a + b)(a − b) to find 54² − 5².
13. 13.Use (a + b)² = a² + 2ab + b² to find 83².
14. 14.Use (a + b)(a − b) = a² − b² to find 96 × 84.
15. 15.Use (a + b)(a − b) = a² − b² to find 91 × 89.
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 58².
17. 17.Use (a + b)² = a² + 2ab + b² to find 35².
18. 18.Use (a + b)(a − b) = a² − b² to find 62 × 58.
19. 19.Use (a − b)² = a² − 2ab + b² to find 75².
20. 20.Use (a + b)(a − b) = a² − b² to find 26 × 14.
21. 21.Use (a − b)² = a² − 2ab + b² to find 72².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 10.
23. 23.If a + b = 10 and ab = 24, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 56² − 28².
25. 25.Use (a + b)² = a² + 2ab + b² to find 43².
26. 26.Find the value of x² − y² when x = 4 and y = 3.
27. 27.Use (a + b)² = a² + 2ab + b² to find 59².
28. 28.Find the value of x² − y² when x = 5 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 85².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 3.
31. 31.Use a² − b² = (a + b)(a − b) to find 25² − 4².
32. 32.Find the value of x² − 2xy + y² when x = 3 and y = 1.
33. 33.If a + b = 6 and ab = 5, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 21².
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 4.
36. 36.Use (a − b)² = a² − 2ab + b² to find 65².
37. 37.Use (a + b)² = a² + 2ab + b² to find 48².
38. 38.If a + b = 5 and ab = 4, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 2.
40. 40.Use (a + b)² = a² + 2ab + b² to find 28².

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