Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 55 · 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 a² − b² = (a + b)(a − b) to find 30² − 9².
2. 2.Use (a − b)² = a² − 2ab + b² to find 87².
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 4.
4. 4.Use (a + b)² = a² + 2ab + b² to find 39².
5. 5.Use (a + b)² = a² + 2ab + b² to find 24².
6. 6.Find the value of x² + 2xy + y² when x = 3 and y = 2.
7. 7.Use (a − b)² = a² − 2ab + b² to find 18².
8. 8.If a − b = 2 and ab = 48, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 1.
10. 10.If a + b = 15 and ab = 44, what is a² + b²?
11. 11.If a − b = 2 and ab = 8, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 7 and y = 2.
13. 13.Use (a − b)² = a² − 2ab + b² to find 37².
14. 14.Find the value of x² + 2xy + y² when x = 12 and y = 5.
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.Use a² − b² = (a + b)(a − b) to find 21² − 16².
17. 17.If a − b = 2 and ab = 3, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 92² − 81².
19. 19.Use (a + b)(a − b) = a² − b² to find 109 × 91.
20. 20.Use (a + b)(a − b) = a² − b² to find 25 × 15.
21. 21.If a + b = 11 and ab = 28, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 92².
23. 23.Use (a − b)² = a² − 2ab + b² to find 97².
24. 24.Use (a + b)(a − b) = a² − b² to find 42 × 38.
25. 25.Use (a + b)(a − b) = a² − b² to find 51 × 49.
26. 26.If a + b = 14 and ab = 48, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 40² − 13².
28. 28.Find the value of x² − y² when x = 3 and y = 1.
29. 29.Use (a + b)(a − b) = a² − b² to find 71 × 69.
30. 30.Use a² − b² = (a + b)(a − b) to find 41² − 19².
31. 31.Use (a + b)(a − b) = a² − b² to find 48 × 32.
32. 32.Use (a + b)² = a² + 2ab + b² to find 72².
33. 33.Use (a + b)² = a² + 2ab + b² to find 99².
34. 34.Use a² − b² = (a + b)(a − b) to find 90² − 65².
35. 35.Use (a + b)² = a² + 2ab + b² to find 74².
36. 36.Use a² − b² = (a + b)(a − b) to find 95² − 77².
37. 37.Use (a − b)² = a² − 2ab + b² to find 64².
38. 38.Use (a + b)² = a² + 2ab + b² to find 32².
39. 39.If a − b = 6 and ab = 27, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 60² − 37².

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