Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 185 · 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 79 × 61.
2. 2.Use (a + b)(a − b) = a² − b² to find 73 × 67.
3. 3.Use (a + b)(a − b) = a² − b² to find 81 × 79.
4. 4.Use a² − b² = (a + b)(a − b) to find 44² − 14².
5. 5.Use (a − b)² = a² − 2ab + b² to find 98².
6. 6.Find the value of x² − y² when x = 6 and y = 4.
7. 7.If a − b = 3 and ab = 4, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 3.
9. 9.Find the value of x² − 2xy + y² when x = 5 and y = 3.
10. 10.Use a² − b² = (a + b)(a − b) to find 94² − 27².
11. 11.Find the value of x² − y² when x = 4 and y = 2.
12. 12.If a + b = 8 and ab = 7, what is a² + b²?
13. 13.Find the value of x² − y² when x = 6 and y = 5.
14. 14.Find the value of x² − 2xy + y² when x = 14 and y = 6.
15. 15.Use (a − b)² = a² − 2ab + b² to find 19².
16. 16.Use (a + b)² = a² + 2ab + b² to find 41².
17. 17.Use (a + b)² = a² + 2ab + b² to find 65².
18. 18.Use (a + b)² = a² + 2ab + b² to find 15².
19. 19.Find the value of x² − y² when x = 5 and y = 4.
20. 20.If a + b = 7 and ab = 10, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 82 × 78.
22. 22.Use (a + b)² = a² + 2ab + b² to find 44².
23. 23.Use a² − b² = (a + b)(a − b) to find 41² − 1².
24. 24.Use (a + b)² = a² + 2ab + b² to find 79².
25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 4.
26. 26.Use a² − b² = (a + b)(a − b) to find 32² − 26².
27. 27.Find the value of x² − 2xy + y² when x = 3 and y = 1.
28. 28.If a − b = 2 and ab = 3, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 12 and y = 11.
30. 30.Use (a + b)(a − b) = a² − b² to find 106 × 94.
31. 31.Use (a − b)² = a² − 2ab + b² to find 46².
32. 32.Find the value of x² + 2xy + y² when x = 15 and y = 9.
33. 33.Find the value of x² − y² when x = 7 and y = 3.
34. 34.If a − b = 4 and ab = 5, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 52².
37. 37.Find the value of x² + 2xy + y² when x = 3 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 72² − 37².
39. 39.Use (a + b)(a − b) = a² − b² to find 62 × 58.
40. 40.Find the value of x² + 2xy + y² when x = 13 and y = 7.

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