Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 589 · 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 37 × 23.
2. 2.If a + b = 19 and ab = 90, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 41².
4. 4.Find the value of x² − y² when x = 8 and y = 7.
5. 5.Find the value of x² − 2xy + y² when x = 9 and y = 2.
6. 6.Use (a + b)(a − b) = a² − b² to find 63 × 57.
7. 7.Use (a + b)(a − b) = a² − b² to find 95 × 85.
8. 8.Use (a − b)² = a² − 2ab + b² to find 39².
9. 9.If a + b = 17 and ab = 72, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 72².
11. 11.Use a² − b² = (a + b)(a − b) to find 88² − 42².
12. 12.Use (a − b)² = a² − 2ab + b² to find 91².
13. 13.Use (a − b)² = a² − 2ab + b² to find 68².
14. 14.If a − b = 1 and ab = 12, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 76² − 41².
16. 16.Use (a − b)² = a² − 2ab + b² to find 23².
17. 17.Use (a + b)² = a² + 2ab + b² to find 75².
18. 18.If a − b = 2 and ab = 8, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 27².
20. 20.Use (a + b)² = a² + 2ab + b² to find 47².
21. 21.Find the value of x² + 2xy + y² when x = 8 and y = 7.
22. 22.If a + b = 9 and ab = 14, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 93².
24. 24.Use (a + b)² = a² + 2ab + b² to find 46².
25. 25.Use (a − b)² = a² − 2ab + b² to find 26².
26. 26.Use (a + b)² = a² + 2ab + b² to find 92².
27. 27.Use (a + b)² = a² + 2ab + b² to find 15².
28. 28.Use (a + b)(a − b) = a² − b² to find 34 × 26.
29. 29.Use (a + b)² = a² + 2ab + b² to find 79².
30. 30.Use (a + b)(a − b) = a² − b² to find 32 × 28.
31. 31.Use (a − b)² = a² − 2ab + b² to find 54².
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Find the value of x² − y² when x = 4 and y = 1.
34. 34.If a − b = 2 and ab = 24, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 99².
36. 36.Use (a + b)² = a² + 2ab + b² to find 35².
37. 37.Use (a + b)² = a² + 2ab + b² to find 65².
38. 38.Use a² − b² = (a + b)(a − b) to find 31² − 7².
39. 39.Use (a + b)² = a² + 2ab + b² to find 64².
40. 40.Use a² − b² = (a + b)(a − b) to find 53² − 51².

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