Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 9 · 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 = 5 and ab = 4, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 74 × 66.
3. 3.Find the value of x² − 2xy + y² when x = 5 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 77² − 11².
5. 5.Use (a + b)(a − b) = a² − b² to find 101 × 99.
6. 6.Use a² − b² = (a + b)(a − b) to find 60² − 58².
7. 7.Find the value of x² − y² when x = 15 and y = 3.
8. 8.Use (a − b)² = a² − 2ab + b² to find 14².
9. 9.Use (a + b)² = a² + 2ab + b² to find 56².
10. 10.Use a² − b² = (a + b)(a − b) to find 62² − 44².
11. 11.Use (a − b)² = a² − 2ab + b² to find 85².
12. 12.Use (a + b)(a − b) = a² − b² to find 38 × 22.
13. 13.Use (a − b)² = a² − 2ab + b² to find 57².
14. 14.If a − b = 1 and ab = 72, what is a² + b²?
15. 15.If a + b = 14 and ab = 48, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 76².
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 4.
18. 18.Use (a + b)² = a² + 2ab + b² to find 64².
19. 19.Use a² − b² = (a + b)(a − b) to find 43² − 15².
20. 20.Use (a + b)² = a² + 2ab + b² to find 31².
21. 21.Use (a − b)² = a² − 2ab + b² to find 54².
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 48².
24. 24.Use (a + b)(a − b) = a² − b² to find 99 × 81.
25. 25.Use (a + b)(a − b) = a² − b² to find 67 × 53.
26. 26.Use (a − b)² = a² − 2ab + b² to find 59².
27. 27.Use a² − b² = (a + b)(a − b) to find 52² − 9².
28. 28.If a − b = 2 and ab = 35, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 59².
30. 30.Use a² − b² = (a + b)(a − b) to find 85² − 4².
31. 31.Use (a + b)(a − b) = a² − b² to find 84 × 76.
32. 32.Use a² − b² = (a + b)(a − b) to find 26² − 8².
33. 33.Find the value of x² + 2xy + y² when x = 7 and y = 2.
34. 34.Use (a + b)² = a² + 2ab + b² to find 79².
35. 35.Find the value of x² − y² when x = 9 and y = 5.
36. 36.Use (a + b)(a − b) = a² − b² to find 28 × 12.
37. 37.Use (a + b)² = a² + 2ab + b² to find 57².
38. 38.Find the value of x² − y² when x = 9 and y = 2.
39. 39.Use (a + b)(a − b) = a² − b² to find 86 × 74.
40. 40.Use (a + b)(a − b) = a² − b² to find 76 × 64.

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