Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 304 · 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 = 1 and ab = 30, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 35².
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 4.
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 42² − 9².
6. 6.Use (a + b)(a − b) = a² − b² to find 21 × 19.
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 103².
9. 9.Use (a + b)² = a² + 2ab + b² to find 53².
10. 10.Use a² − b² = (a + b)(a − b) to find 34² − 31².
11. 11.Use a² − b² = (a + b)(a − b) to find 70² − 19².
12. 12.Use (a + b)(a − b) = a² − b² to find 33 × 27.
13. 13.Use (a + b)(a − b) = a² − b² to find 34 × 26.
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 8.
15. 15.If a − b = 4 and ab = 21, what is a² + b²?
16. 16.Find the value of x² + 2xy + y² when x = 4 and y = 1.
17. 17.Find the value of x² − 2xy + y² when x = 4 and y = 3.
18. 18.Use a² − b² = (a + b)(a − b) to find 92² − 3².
19. 19.If a − b = 1 and ab = 12, what is a² + b²?
20. 20.If a + b = 13 and ab = 22, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 29².
22. 22.Use (a + b)(a − b) = a² − b² to find 25 × 15.
23. 23.Use a² − b² = (a + b)(a − b) to find 60² − 58².
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 4.
25. 25.Use (a + b)(a − b) = a² − b² to find 71 × 69.
26. 26.Use (a + b)² = a² + 2ab + b² to find 21².
27. 27.Use (a + b)² = a² + 2ab + b² to find 45².
28. 28.Use (a − b)² = a² − 2ab + b² to find 17².
29. 29.Use a² − b² = (a + b)(a − b) to find 69² − 46².
30. 30.Use (a + b)(a − b) = a² − b² to find 29 × 11.
31. 31.Use a² − b² = (a + b)(a − b) to find 97² − 66².
32. 32.Use a² − b² = (a + b)(a − b) to find 65² − 12².
33. 33.Use (a + b)(a − b) = a² − b² to find 36 × 24.
34. 34.Use (a + b)² = a² + 2ab + b² to find 107².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 2.
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 48² − 29².
38. 38.Use (a + b)² = a² + 2ab + b² to find 59².
39. 39.Use (a − b)² = a² − 2ab + b² to find 18².
40. 40.Use a² − b² = (a + b)(a − b) to find 52² − 26².

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