Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 213 · 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 21² − 17².
2. 2.Find the value of x² − y² when x = 3 and y = 2.
3. 3.Use a² − b² = (a + b)(a − b) to find 27² − 1².
4. 4.Find the value of x² − 2xy + y² when x = 9 and y = 6.
5. 5.Use (a − b)² = a² − 2ab + b² to find 68².
6. 6.Use a² − b² = (a + b)(a − b) to find 40² − 7².
7. 7.Use (a + b)(a − b) = a² − b² to find 36 × 24.
8. 8.Use a² − b² = (a + b)(a − b) to find 43² − 19².
9. 9.If a − b = 3 and ab = 4, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 13.
11. 11.Use a² − b² = (a + b)(a − b) to find 42² − 19².
12. 12.If a + b = 18 and ab = 72, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 104².
14. 14.If a − b = 3 and ab = 18, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 39².
16. 16.If a + b = 15 and ab = 56, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 71 × 69.
19. 19.Find the value of x² − 2xy + y² when x = 3 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 93² − 42².
21. 21.Use (a − b)² = a² − 2ab + b² to find 41².
22. 22.Use (a + b)(a − b) = a² − b² to find 104 × 96.
23. 23.Use (a − b)² = a² − 2ab + b² to find 33².
24. 24.Use (a − b)² = a² − 2ab + b² to find 76².
25. 25.Use a² − b² = (a + b)(a − b) to find 53² − 16².
26. 26.If a − b = 1 and ab = 6, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 15².
28. 28.Use (a + b)² = a² + 2ab + b² to find 36².
29. 29.Find the value of x² − y² when x = 14 and y = 5.
30. 30.Use (a + b)² = a² + 2ab + b² to find 103².
31. 31.If a − b = 1 and ab = 2, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 47².
33. 33.Use (a + b)² = a² + 2ab + b² to find 106².
34. 34.Use (a + b)(a − b) = a² − b² to find 89 × 71.
35. 35.Use (a + b)² = a² + 2ab + b² to find 16².
36. 36.Use (a − b)² = a² − 2ab + b² to find 49².
37. 37.If a + b = 8 and ab = 12, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 70² − 32².
39. 39.If a + b = 7 and ab = 6, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 49².

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