Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 159 · 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.If a + b = 6 and ab = 5, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 15².
5. 5.Use (a + b)(a − b) = a² − b² to find 38 × 22.
6. 6.Use a² − b² = (a + b)(a − b) to find 40² − 25².
7. 7.Use (a + b)² = a² + 2ab + b² to find 32².
8. 8.Use (a + b)(a − b) = a² − b² to find 45 × 35.
9. 9.Use (a + b)² = a² + 2ab + b² to find 12².
10. 10.Use (a − b)² = a² − 2ab + b² to find 13².
11. 11.Use a² − b² = (a + b)(a − b) to find 94² − 35².
12. 12.Use a² − b² = (a + b)(a − b) to find 51² − 34².
13. 13.Use (a + b)(a − b) = a² − b² to find 26 × 14.
14. 14.Use (a − b)² = a² − 2ab + b² to find 87².
15. 15.Use (a − b)² = a² − 2ab + b² to find 99².
16. 16.Use (a + b)² = a² + 2ab + b² to find 41².
17. 17.Find the value of x² − y² when x = 15 and y = 1.
18. 18.If a + b = 10 and ab = 24, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 8 and y = 1.
20. 20.Use (a + b)² = a² + 2ab + b² to find 61².
21. 21.Use (a − b)² = a² − 2ab + b² to find 81².
22. 22.Use a² − b² = (a + b)(a − b) to find 71² − 38².
23. 23.Use (a + b)(a − b) = a² − b² to find 24 × 16.
24. 24.Use (a + b)² = a² + 2ab + b² to find 45².
25. 25.Use (a + b)(a − b) = a² − b² to find 106 × 94.
26. 26.Use (a + b)(a − b) = a² − b² to find 37 × 23.
27. 27.Find the value of x² − 2xy + y² when x = 3 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 83².
29. 29.Use (a + b)(a − b) = a² − b² to find 36 × 24.
30. 30.Find the value of x² + 2xy + y² when x = 5 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 91².
32. 32.If a + b = 9 and ab = 8, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 78².
34. 34.Use (a + b)² = a² + 2ab + b² to find 86².
35. 35.Use (a + b)(a − b) = a² − b² to find 87 × 73.
36. 36.Use (a − b)² = a² − 2ab + b² to find 93².
37. 37.Use (a + b)² = a² + 2ab + b² to find 108².
38. 38.Use (a + b)(a − b) = a² − b² to find 56 × 44.
39. 39.Use a² − b² = (a + b)(a − b) to find 50² − 20².
40. 40.Find the value of x² − 2xy + y² when x = 13 and y = 3.

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