Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 17 · 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 = 72, what is a² + b²?
2. 2.If a − b = 2 and ab = 15, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 93².
4. 4.Use (a + b)² = a² + 2ab + b² to find 34².
5. 5.Find the value of x² − 2xy + y² when x = 11 and y = 2.
6. 6.Find the value of x² − y² when x = 9 and y = 5.
7. 7.Use (a + b)² = a² + 2ab + b² to find 43².
8. 8.Use (a + b)(a − b) = a² − b² to find 93 × 87.
9. 9.If a − b = 4 and ab = 45, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 97².
11. 11.Use (a + b)² = a² + 2ab + b² to find 93².
12. 12.If a − b = 6 and ab = 55, what is a² + b²?
13. 13.If a − b = 2 and ab = 8, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 26² − 11².
15. 15.Find the value of x² − 2xy + y² when x = 10 and y = 3.
16. 16.Use (a + b)(a − b) = a² − b² to find 62 × 58.
17. 17.Use (a − b)² = a² − 2ab + b² to find 99².
18. 18.Use (a − b)² = a² − 2ab + b² to find 38².
19. 19.Use (a + b)(a − b) = a² − b² to find 47 × 33.
20. 20.Use (a − b)² = a² − 2ab + b² to find 85².
21. 21.Use (a + b)(a − b) = a² − b² to find 21 × 19.
22. 22.Use (a + b)(a − b) = a² − b² to find 85 × 75.
23. 23.Use (a + b)² = a² + 2ab + b² to find 18².
24. 24.If a − b = 9 and ab = 22, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 70² − 54².
26. 26.Use (a + b)(a − b) = a² − b² to find 35 × 25.
27. 27.Use (a + b)² = a² + 2ab + b² to find 12².
28. 28.Use a² − b² = (a + b)(a − b) to find 68² − 18².
29. 29.Use (a + b)² = a² + 2ab + b² to find 51².
30. 30.Use (a + b)² = a² + 2ab + b² to find 39².
31. 31.Use a² − b² = (a + b)(a − b) to find 22² − 7².
32. 32.Find the value of x² − 2xy + y² when x = 3 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 98².
34. 34.Find the value of x² + 2xy + y² when x = 10 and y = 7.
35. 35.Use (a − b)² = a² − 2ab + b² to find 48².
36. 36.Use (a − b)² = a² − 2ab + b² to find 96².
37. 37.Use (a + b)(a − b) = a² − b² to find 107 × 93.
38. 38.Use (a + b)(a − b) = a² − b² to find 101 × 99.
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 42² − 40².

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