Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 593 · 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 48² − 16².
2. 2.Use (a − b)² = a² − 2ab + b² to find 91².
3. 3.If a + b = 5 and ab = 6, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 93².
5. 5.Use (a − b)² = a² − 2ab + b² to find 18².
6. 6.Use (a + b)² = a² + 2ab + b² to find 98².
7. 7.Use a² − b² = (a + b)(a − b) to find 84² − 36².
8. 8.Use (a − b)² = a² − 2ab + b² to find 48².
9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 87².
11. 11.Use (a + b)(a − b) = a² − b² to find 31 × 29.
12. 12.Find the value of x² − y² when x = 5 and y = 1.
13. 13.Use (a + b)(a − b) = a² − b² to find 77 × 63.
14. 14.Use a² − b² = (a + b)(a − b) to find 79² − 73².
15. 15.If a − b = 2 and ab = 35, what is a² + b²?
16. 16.Find the value of x² + 2xy + y² when x = 5 and y = 3.
17. 17.Use a² − b² = (a + b)(a − b) to find 85² − 70².
18. 18.Use a² − b² = (a + b)(a − b) to find 44² − 31².
19. 19.Use (a − b)² = a² − 2ab + b² to find 26².
20. 20.Use (a + b)(a − b) = a² − b² to find 108 × 92.
21. 21.Find the value of x² + 2xy + y² when x = 13 and y = 12.
22. 22.Find the value of x² − 2xy + y² when x = 12 and y = 8.
23. 23.Use (a − b)² = a² − 2ab + b² to find 88².
24. 24.Use (a + b)² = a² + 2ab + b² to find 61².
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.Use (a − b)² = a² − 2ab + b² to find 29².
27. 27.Find the value of x² − 2xy + y² when x = 13 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 67².
29. 29.Find the value of x² − y² when x = 9 and y = 2.
30. 30.Find the value of x² − y² when x = 3 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 103².
32. 32.Use (a + b)² = a² + 2ab + b² to find 74².
33. 33.Find the value of x² − y² when x = 12 and y = 10.
34. 34.If a − b = 1 and ab = 2, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 76².
36. 36.If a − b = 7 and ab = 44, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 12 and y = 9.
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 26² − 13².
40. 40.Use (a + b)² = a² + 2ab + b² to find 53².

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