Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 541 · 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)(a − b) = a² − b² to find 69 × 51.
2. 2.Use (a + b)² = a² + 2ab + b² to find 88².
3. 3.Use (a + b)² = a² + 2ab + b² to find 77².
4. 4.Use (a + b)(a − b) = a² − b² to find 65 × 55.
5. 5.Find the value of x² − 2xy + y² when x = 6 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
7. 7.Use (a + b)² = a² + 2ab + b² to find 54².
8. 8.Use a² − b² = (a + b)(a − b) to find 85² − 38².
9. 9.If a − b = 3 and ab = 10, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 87² − 85².
11. 11.Use (a − b)² = a² − 2ab + b² to find 41².
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 1.
13. 13.Find the value of x² − 2xy + y² when x = 8 and y = 7.
14. 14.Use (a − b)² = a² − 2ab + b² to find 87².
15. 15.Use (a − b)² = a² − 2ab + b² to find 89².
16. 16.Use a² − b² = (a + b)(a − b) to find 56² − 52².
17. 17.Use a² − b² = (a + b)(a − b) to find 85² − 39².
18. 18.Find the value of x² + 2xy + y² when x = 6 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 51².
20. 20.Use (a + b)² = a² + 2ab + b² to find 18².
21. 21.Find the value of x² − y² when x = 6 and y = 1.
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Use (a − b)² = a² − 2ab + b² to find 93².
24. 24.Use (a + b)(a − b) = a² − b² to find 57 × 43.
25. 25.Use (a − b)² = a² − 2ab + b² to find 32².
26. 26.If a + b = 6 and ab = 8, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 29².
28. 28.Use a² − b² = (a + b)(a − b) to find 72² − 63².
29. 29.Use (a − b)² = a² − 2ab + b² to find 98².
30. 30.Use (a + b)(a − b) = a² − b² to find 83 × 77.
31. 31.Use (a + b)(a − b) = a² − b² to find 62 × 58.
32. 32.Use (a + b)² = a² + 2ab + b² to find 21².
33. 33.Find the value of x² − 2xy + y² when x = 7 and y = 1.
34. 34.Use (a − b)² = a² − 2ab + b² to find 79².
35. 35.Use a² − b² = (a + b)(a − b) to find 39² − 3².
36. 36.Use (a + b)(a − b) = a² − b² to find 107 × 93.
37. 37.If a − b = 9 and ab = 10, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 26².
39. 39.If a − b = 2 and ab = 99, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 23² − 12².

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