Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 380 · 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 − y² when x = 13 and y = 3.
2. 2.Find the value of x² − y² when x = 13 and y = 7.
3. 3.Find the value of x² − 2xy + y² when x = 7 and y = 3.
4. 4.If a + b = 12 and ab = 11, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 78 × 62.
6. 6.Use (a + b)² = a² + 2ab + b² to find 36².
7. 7.Use (a + b)(a − b) = a² − b² to find 87 × 73.
8. 8.Use (a + b)(a − b) = a² − b² to find 73 × 67.
9. 9.Find the value of x² − 2xy + y² when x = 14 and y = 7.
10. 10.Use a² − b² = (a + b)(a − b) to find 44² − 27².
11. 11.If a − b = 1 and ab = 2, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 102².
13. 13.Use (a − b)² = a² − 2ab + b² to find 44².
14. 14.Use (a − b)² = a² − 2ab + b² to find 41².
15. 15.Use (a + b)² = a² + 2ab + b² to find 44².
16. 16.Use (a + b)(a − b) = a² − b² to find 49 × 31.
17. 17.Use a² − b² = (a + b)(a − b) to find 83² − 57².
18. 18.Use (a + b)(a − b) = a² − b² to find 43 × 37.
19. 19.Use (a − b)² = a² − 2ab + b² to find 54².
20. 20.Use a² − b² = (a + b)(a − b) to find 58² − 10².
21. 21.Use a² − b² = (a + b)(a − b) to find 46² − 40².
22. 22.Find the value of x² − y² when x = 7 and y = 6.
23. 23.Use (a − b)² = a² − 2ab + b² to find 17².
24. 24.Use (a − b)² = a² − 2ab + b² to find 13².
25. 25.Use (a + b)(a − b) = a² − b² to find 21 × 19.
26. 26.Use (a + b)(a − b) = a² − b² to find 22 × 18.
27. 27.Use (a + b)² = a² + 2ab + b² to find 26².
28. 28.Use a² − b² = (a + b)(a − b) to find 40² − 19².
29. 29.Find the value of x² + 2xy + y² when x = 10 and y = 2.
30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
31. 31.Use (a − b)² = a² − 2ab + b² to find 82².
32. 32.Use (a + b)² = a² + 2ab + b² to find 87².
33. 33.Use a² − b² = (a + b)(a − b) to find 98² − 81².
34. 34.Use (a − b)² = a² − 2ab + b² to find 72².
35. 35.Use (a − b)² = a² − 2ab + b² to find 85².
36. 36.Use a² − b² = (a + b)(a − b) to find 90² − 53².
37. 37.Use (a − b)² = a² − 2ab + b² to find 77².
38. 38.Use a² − b² = (a + b)(a − b) to find 64² − 45².
39. 39.Use (a + b)(a − b) = a² − b² to find 74 × 66.
40. 40.If a + b = 8 and ab = 7, what is a² + b²?

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