Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 78 · 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 39² − 3².
2. 2.Use (a − b)² = a² − 2ab + b² to find 99².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 59².
4. 4.Use (a + b)(a − b) = a² − b² to find 91 × 89.
5. 5.Use a² − b² = (a + b)(a − b) to find 57² − 37².
6. 6.Use (a − b)² = a² − 2ab + b² to find 93².
7. 7.Use (a + b)² = a² + 2ab + b² to find 12².
8. 8.If a + b = 13 and ab = 30, what is a² + b²?
9. 9.If a − b = 1 and ab = 20, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 22² − 8².
11. 11.Use (a + b)(a − b) = a² − b² to find 22 × 18.
12. 12.Use (a + b)(a − b) = a² − b² to find 68 × 52.
13. 13.Use a² − b² = (a + b)(a − b) to find 92² − 47².
14. 14.Use (a + b)(a − b) = a² − b² to find 105 × 95.
15. 15.Use (a − b)² = a² − 2ab + b² to find 87².
16. 16.Use (a + b)² = a² + 2ab + b² to find 31².
17. 17.Find the value of x² + 2xy + y² when x = 7 and y = 6.
18. 18.Use (a + b)(a − b) = a² − b² to find 72 × 68.
19. 19.Use (a + b)(a − b) = a² − b² to find 92 × 88.
20. 20.Use (a + b)² = a² + 2ab + b² to find 25².
21. 21.Use (a − b)² = a² − 2ab + b² to find 66².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 1.
23. 23.If a + b = 14 and ab = 48, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 79² − 9².
25. 25.Use (a + b)(a − b) = a² − b² to find 52 × 48.
26. 26.Use a² − b² = (a + b)(a − b) to find 37² − 23².
27. 27.Find the value of x² + 2xy + y² when x = 13 and y = 6.
28. 28.Use a² − b² = (a + b)(a − b) to find 31² − 21².
29. 29.Use (a − b)² = a² − 2ab + b² to find 78².
30. 30.If a − b = 6 and ab = 16, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 58².
32. 32.Use (a − b)² = a² − 2ab + b² to find 79².
33. 33.Use (a + b)² = a² + 2ab + b² to find 84².
34. 34.Use a² − b² = (a + b)(a − b) to find 42² − 22².
35. 35.Use (a + b)(a − b) = a² − b² to find 63 × 57.
36. 36.Use (a + b)(a − b) = a² − b² to find 47 × 33.
37. 37.Use (a + b)² = a² + 2ab + b² to find 69².
38. 38.Use (a + b)² = a² + 2ab + b² to find 109².
39. 39.Use a² − b² = (a + b)(a − b) to find 33² − 12².
40. 40.Use a² − b² = (a + b)(a − b) to find 33² − 26².

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