Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 998 · 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 86 × 74.
2. 2.Use (a + b)(a − b) = a² − b² to find 25 × 15.
3. 3.Use (a + b)² = a² + 2ab + b² to find 47².
4. 4.Use (a + b)² = a² + 2ab + b² to find 78².
5. 5.Use (a − b)² = a² − 2ab + b² to find 67².
6. 6.Use (a − b)² = a² − 2ab + b² to find 14².
7. 7.If a − b = 1 and ab = 132, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 99².
9. 9.Use (a + b)(a − b) = a² − b² to find 31 × 29.
10. 10.Use (a + b)(a − b) = a² − b² to find 87 × 73.
11. 11.Use (a − b)² = a² − 2ab + b² to find 59².
12. 12.Use (a + b)(a − b) = a² − b² to find 32 × 28.
13. 13.Use (a + b)(a − b) = a² − b² to find 48 × 32.
14. 14.Use (a + b)(a − b) = a² − b² to find 103 × 97.
15. 15.Use (a + b)² = a² + 2ab + b² to find 13².
16. 16.Use (a + b)² = a² + 2ab + b² to find 79².
17. 17.Use a² − b² = (a + b)(a − b) to find 80² − 3².
18. 18.If a − b = 9 and ab = 22, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 16².
20. 20.Find the value of x² − 2xy + y² when x = 11 and y = 7.
21. 21.Use (a + b)(a − b) = a² − b² to find 67 × 53.
22. 22.Use (a + b)(a − b) = a² − b² to find 42 × 38.
23. 23.Use (a − b)² = a² − 2ab + b² to find 61².
24. 24.Use (a + b)(a − b) = a² − b² to find 52 × 48.
25. 25.Use (a + b)² = a² + 2ab + b² to find 75².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 73² − 65².
28. 28.Use (a + b)(a − b) = a² − b² to find 47 × 33.
29. 29.If a − b = 1 and ab = 20, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 103².
31. 31.Use (a + b)² = a² + 2ab + b² to find 74².
32. 32.Use a² − b² = (a + b)(a − b) to find 47² − 38².
33. 33.Find the value of x² − y² when x = 7 and y = 6.
34. 34.Use (a + b)(a − b) = a² − b² to find 102 × 98.
35. 35.Find the value of x² − y² when x = 6 and y = 1.
36. 36.Use (a + b)(a − b) = a² − b² to find 74 × 66.
37. 37.Find the value of x² − 2xy + y² when x = 6 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 42² − 34².
39. 39.Find the value of x² − y² when x = 15 and y = 13.
40. 40.Use a² − b² = (a + b)(a − b) to find 53² − 22².

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