Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 698 · 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)² = a² + 2ab + b² to find 21².
2. 2.Use a² − b² = (a + b)(a − b) to find 93² − 53².
3. 3.If a + b = 17 and ab = 72, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 72².
5. 5.If a − b = 1 and ab = 30, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 45².
7. 7.Find the value of x² + 2xy + y² when x = 13 and y = 3.
8. 8.Use (a + b)² = a² + 2ab + b² to find 91².
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 81².
11. 11.If a + b = 6 and ab = 5, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 104 × 96.
13. 13.Use (a − b)² = a² − 2ab + b² to find 47².
14. 14.Use (a + b)(a − b) = a² − b² to find 76 × 64.
15. 15.Find the value of x² − 2xy + y² when x = 11 and y = 2.
16. 16.Find the value of x² + 2xy + y² when x = 9 and y = 8.
17. 17.If a − b = 1 and ab = 2, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 79².
19. 19.Use (a − b)² = a² − 2ab + b² to find 33².
20. 20.Use a² − b² = (a + b)(a − b) to find 96² − 52².
21. 21.Use (a + b)² = a² + 2ab + b² to find 37².
22. 22.Use a² − b² = (a + b)(a − b) to find 29² − 27².
23. 23.Use a² − b² = (a + b)(a − b) to find 46² − 15².
24. 24.Use a² − b² = (a + b)(a − b) to find 89² − 32².
25. 25.Use (a − b)² = a² − 2ab + b² to find 17².
26. 26.Use (a + b)(a − b) = a² − b² to find 42 × 38.
27. 27.Use a² − b² = (a + b)(a − b) to find 42² − 35².
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 24 × 16.
30. 30.Use (a − b)² = a² − 2ab + b² to find 98².
31. 31.Use a² − b² = (a + b)(a − b) to find 43² − 25².
32. 32.Use (a + b)² = a² + 2ab + b² to find 52².
33. 33.If a + b = 8 and ab = 12, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 62².
35. 35.Find the value of x² − y² when x = 13 and y = 11.
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 5.
37. 37.Use (a + b)(a − b) = a² − b² to find 106 × 94.
38. 38.Use a² − b² = (a + b)(a − b) to find 94² − 74².
39. 39.Find the value of x² − 2xy + y² when x = 15 and y = 8.
40. 40.Use a² − b² = (a + b)(a − b) to find 67² − 4².

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