Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 561 · 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 69² − 32².
2. 2.Use (a + b)² = a² + 2ab + b² to find 35².
3. 3.Use (a + b)² = a² + 2ab + b² to find 14².
4. 4.Use a² − b² = (a + b)(a − b) to find 76² − 17².
5. 5.Use (a + b)² = a² + 2ab + b² to find 63².
6. 6.Use (a + b)² = a² + 2ab + b² to find 38².
7. 7.Use (a + b)² = a² + 2ab + b² to find 34².
8. 8.Use a² − b² = (a + b)(a − b) to find 97² − 52².
9. 9.Use a² − b² = (a + b)(a − b) to find 64² − 4².
10. 10.Find the value of x² − 2xy + y² when x = 9 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 57².
12. 12.Use a² − b² = (a + b)(a − b) to find 59² − 26².
13. 13.Use (a − b)² = a² − 2ab + b² to find 17².
14. 14.Use (a + b)² = a² + 2ab + b² to find 57².
15. 15.Use (a + b)² = a² + 2ab + b² to find 73².
16. 16.Use a² − b² = (a + b)(a − b) to find 91² − 26².
17. 17.Use (a + b)(a − b) = a² − b² to find 58 × 42.
18. 18.Use (a + b)² = a² + 2ab + b² to find 75².
19. 19.If a − b = 1 and ab = 2, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 92² − 80².
21. 21.Use a² − b² = (a + b)(a − b) to find 48² − 18².
22. 22.Use (a + b)(a − b) = a² − b² to find 84 × 76.
23. 23.Use a² − b² = (a + b)(a − b) to find 20² − 5².
24. 24.Use (a + b)² = a² + 2ab + b² to find 29².
25. 25.Use (a + b)² = a² + 2ab + b² to find 51².
26. 26.Use (a + b)(a − b) = a² − b² to find 86 × 74.
27. 27.Use (a + b)(a − b) = a² − b² to find 54 × 46.
28. 28.Use a² − b² = (a + b)(a − b) to find 93² − 76².
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 1.
30. 30.Use (a − b)² = a² − 2ab + b² to find 67².
31. 31.Use (a + b)² = a² + 2ab + b² to find 91².
32. 32.Use (a + b)(a − b) = a² − b² to find 94 × 86.
33. 33.Use (a + b)² = a² + 2ab + b² to find 43².
34. 34.Use (a − b)² = a² − 2ab + b² to find 99².
35. 35.Use (a + b)² = a² + 2ab + b² to find 109².
36. 36.If a + b = 16 and ab = 48, what is a² + b²?
37. 37.Find the value of x² − y² when x = 11 and y = 9.
38. 38.If a − b = 2 and ab = 15, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 16².
40. 40.Use (a − b)² = a² − 2ab + b² to find 94².

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