Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 557 · 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 52 × 48.
2. 2.If a − b = 5 and ab = 84, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 66² − 44².
4. 4.Use a² − b² = (a + b)(a − b) to find 89² − 30².
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 9.
6. 6.Use (a + b)² = a² + 2ab + b² to find 49².
7. 7.Use (a + b)(a − b) = a² − b² to find 32 × 28.
8. 8.Use a² − b² = (a + b)(a − b) to find 62² − 25².
9. 9.Use (a + b)(a − b) = a² − b² to find 57 × 43.
10. 10.Use (a + b)² = a² + 2ab + b² to find 45².
11. 11.Use (a − b)² = a² − 2ab + b² to find 26².
12. 12.If a + b = 11 and ab = 30, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 10 and y = 2.
14. 14.If a − b = 3 and ab = 108, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 67² − 16².
16. 16.Use (a − b)² = a² − 2ab + b² to find 74².
17. 17.Use (a + b)(a − b) = a² − b² to find 86 × 74.
18. 18.Find the value of x² − y² when x = 3 and y = 2.
19. 19.Use a² − b² = (a + b)(a − b) to find 50² − 15².
20. 20.Use (a − b)² = a² − 2ab + b² to find 37².
21. 21.Use (a + b)² = a² + 2ab + b² to find 97².
22. 22.Find the value of x² − y² when x = 12 and y = 9.
23. 23.Use (a + b)² = a² + 2ab + b² to find 46².
24. 24.Use (a − b)² = a² − 2ab + b² to find 24².
25. 25.Use (a + b)² = a² + 2ab + b² to find 93².
26. 26.Use (a + b)(a − b) = a² − b² to find 48 × 32.
27. 27.Find the value of x² − y² when x = 8 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 24² − 12².
29. 29.Use (a + b)² = a² + 2ab + b² to find 65².
30. 30.Use (a + b)² = a² + 2ab + b² to find 68².
31. 31.Use a² − b² = (a + b)(a − b) to find 48² − 35².
32. 32.Use (a − b)² = a² − 2ab + b² to find 21².
33. 33.If a + b = 7 and ab = 12, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 37 × 23.
35. 35.Use (a + b)(a − b) = a² − b² to find 58 × 42.
36. 36.If a + b = 10 and ab = 24, what is a² + b²?
37. 37.If a + b = 13 and ab = 36, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 59².
39. 39.Use (a − b)² = a² − 2ab + b² to find 11².
40. 40.If a + b = 5 and ab = 4, what is a² + b²?

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