Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 177 · 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 97 × 83.
2. 2.Use (a + b)² = a² + 2ab + b² to find 41².
3. 3.Find the value of x² − y² when x = 8 and y = 7.
4. 4.If a + b = 19 and ab = 84, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 67².
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.Use (a + b)(a − b) = a² − b² to find 38 × 22.
8. 8.If a − b = 1 and ab = 12, what is a² + b²?
9. 9.If a − b = 4 and ab = 5, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 104 × 96.
11. 11.Use (a + b)² = a² + 2ab + b² to find 13².
12. 12.Find the value of x² − y² when x = 11 and y = 7.
13. 13.If a − b = 2 and ab = 24, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 44² − 22².
15. 15.Use a² − b² = (a + b)(a − b) to find 93² − 4².
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 18².
17. 17.Use (a + b)(a − b) = a² − b² to find 71 × 69.
18. 18.Use (a − b)² = a² − 2ab + b² to find 64².
19. 19.Use (a − b)² = a² − 2ab + b² to find 47².
20. 20.Use (a + b)² = a² + 2ab + b² to find 17².
21. 21.Use (a − b)² = a² − 2ab + b² to find 98².
22. 22.If a + b = 12 and ab = 27, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 12 and y = 5.
24. 24.Use (a + b)(a − b) = a² − b² to find 72 × 68.
25. 25.Use (a + b)² = a² + 2ab + b² to find 74².
26. 26.Use (a + b)² = a² + 2ab + b² to find 89².
27. 27.Use (a + b)² = a² + 2ab + b² to find 57².
28. 28.If a − b = 2 and ab = 3, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 97² − 56².
30. 30.Find the value of x² − 2xy + y² when x = 11 and y = 6.
31. 31.If a + b = 23 and ab = 132, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 69².
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 1.
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 24².
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 2.
37. 37.Find the value of x² − y² when x = 3 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 82 × 78.
39. 39.Use a² − b² = (a + b)(a − b) to find 91² − 16².
40. 40.Use (a + b)(a − b) = a² − b² to find 44 × 36.

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