Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 71 · 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 88² − 4².
2. 2.Use (a − b)² = a² − 2ab + b² to find 76².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use (a + b)² = a² + 2ab + b² to find 75².
5. 5.Use (a + b)² = a² + 2ab + b² to find 87².
6. 6.If a + b = 10 and ab = 24, what is a² + b²?
7. 7.If a − b = 1 and ab = 20, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 41² − 36².
9. 9.Use (a + b)(a − b) = a² − b² to find 84 × 76.
10. 10.Use (a + b)(a − b) = a² − b² to find 73 × 67.
11. 11.Use (a − b)² = a² − 2ab + b² to find 29².
12. 12.Use (a + b)(a − b) = a² − b² to find 72 × 68.
13. 13.Find the value of x² + 2xy + y² when x = 15 and y = 3.
14. 14.Use (a + b)² = a² + 2ab + b² to find 19².
15. 15.Use (a + b)(a − b) = a² − b² to find 58 × 42.
16. 16.Use (a − b)² = a² − 2ab + b² to find 25².
17. 17.If a − b = 6 and ab = 7, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 6.
19. 19.If a − b = 1 and ab = 2, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 8 and y = 2.
21. 21.Use (a + b)² = a² + 2ab + b² to find 32².
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 6.
23. 23.Use a² − b² = (a + b)(a − b) to find 25² − 14².
24. 24.Use (a + b)(a − b) = a² − b² to find 32 × 28.
25. 25.Find the value of x² − 2xy + y² when x = 3 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 62².
27. 27.Use (a + b)(a − b) = a² − b² to find 99 × 81.
28. 28.Use (a − b)² = a² − 2ab + b² to find 28².
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.If a + b = 4 and ab = 3, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 28².
32. 32.Use (a − b)² = a² − 2ab + b² to find 19².
33. 33.Use (a + b)(a − b) = a² − b² to find 94 × 86.
34. 34.Use (a − b)² = a² − 2ab + b² to find 48².
35. 35.Find the value of x² − y² when x = 11 and y = 9.
36. 36.Use (a + b)(a − b) = a² − b² to find 101 × 99.
37. 37.Find the value of x² + 2xy + y² when x = 15 and y = 7.
38. 38.Use (a − b)² = a² − 2ab + b² to find 14².
39. 39.Use (a + b)² = a² + 2ab + b² to find 91².
40. 40.Use a² − b² = (a + b)(a − b) to find 47² − 21².

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