Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 779 · 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 = 7, what is a² + b²?
2. 2.If a + b = 5 and ab = 4, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 22² − 9².
4. 4.Find the value of x² − y² when x = 11 and y = 10.
5. 5.Use a² − b² = (a + b)(a − b) to find 31² − 6².
6. 6.Use (a − b)² = a² − 2ab + b² to find 47².
7. 7.Find the value of x² − 2xy + y² when x = 3 and y = 1.
8. 8.Use a² − b² = (a + b)(a − b) to find 79² − 77².
9. 9.Use (a + b)(a − b) = a² − b² to find 88 × 72.
10. 10.Use (a + b)(a − b) = a² − b² to find 93 × 87.
11. 11.If a − b = 4 and ab = 45, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 83 × 77.
13. 13.Find the value of x² − y² when x = 4 and y = 1.
14. 14.Find the value of x² − y² when x = 6 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 49².
16. 16.Use (a − b)² = a² − 2ab + b² to find 12².
17. 17.Use (a + b)² = a² + 2ab + b² to find 72².
18. 18.If a + b = 16 and ab = 63, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 108².
20. 20.Use (a − b)² = a² − 2ab + b² to find 65².
21. 21.Use (a + b)² = a² + 2ab + b² to find 78².
22. 22.Use (a + b)(a − b) = a² − b² to find 69 × 51.
23. 23.Use (a + b)² = a² + 2ab + b² to find 101².
24. 24.If a + b = 6 and ab = 5, what is a² + b²?
25. 25.If a + b = 11 and ab = 28, what is a² + b²?
26. 26.Find the value of x² − y² when x = 9 and y = 8.
27. 27.Use (a + b)(a − b) = a² − b² to find 78 × 62.
28. 28.Use (a − b)² = a² − 2ab + b² to find 85².
29. 29.Use a² − b² = (a + b)(a − b) to find 24² − 20².
30. 30.Use a² − b² = (a + b)(a − b) to find 69² − 53².
31. 31.Use (a − b)² = a² − 2ab + b² to find 75².
32. 32.Use (a + b)(a − b) = a² − b² to find 24 × 16.
33. 33.Use (a − b)² = a² − 2ab + b² to find 89².
34. 34.Use (a + b)² = a² + 2ab + b² to find 52².
35. 35.Use (a + b)² = a² + 2ab + b² to find 92².
36. 36.Use a² − b² = (a + b)(a − b) to find 36² − 3².
37. 37.Use (a + b)² = a² + 2ab + b² to find 91².
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 43².
39. 39.Use (a − b)² = a² − 2ab + b² to find 39².
40. 40.If a − b = 1 and ab = 12, what is a² + b²?

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