Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 294 · 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 99².
2. 2.Use a² − b² = (a + b)(a − b) to find 81² − 61².
3. 3.Find the value of x² − y² when x = 3 and y = 1.
4. 4.Use (a + b)(a − b) = a² − b² to find 56 × 44.
5. 5.If a − b = 4 and ab = 96, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 25 × 15.
7. 7.Use a² − b² = (a + b)(a − b) to find 31² − 24².
8. 8.Use (a + b)² = a² + 2ab + b² to find 26².
9. 9.Use (a + b)(a − b) = a² − b² to find 46 × 34.
10. 10.Use (a + b)² = a² + 2ab + b² to find 39².
11. 11.Use a² − b² = (a + b)(a − b) to find 24² − 15².
12. 12.If a + b = 15 and ab = 36, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 104 × 96.
14. 14.Use (a − b)² = a² − 2ab + b² to find 69².
15. 15.Find the value of x² − y² when x = 15 and y = 6.
16. 16.Use (a + b)(a − b) = a² − b² to find 36 × 24.
17. 17.Use (a + b)(a − b) = a² − b² to find 34 × 26.
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 7.
19. 19.Use a² − b² = (a + b)(a − b) to find 34² − 33².
20. 20.Use (a − b)² = a² − 2ab + b² to find 47².
21. 21.Find the value of x² − y² when x = 11 and y = 2.
22. 22.Use (a + b)² = a² + 2ab + b² to find 97².
23. 23.Find the value of x² − 2xy + y² when x = 14 and y = 10.
24. 24.Use (a + b)(a − b) = a² − b² to find 37 × 23.
25. 25.If a + b = 18 and ab = 77, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 91² − 9².
27. 27.Find the value of x² − 2xy + y² when x = 6 and y = 4.
28. 28.Find the value of x² + 2xy + y² when x = 5 and y = 3.
29. 29.Find the value of x² + 2xy + y² when x = 11 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 92 × 88.
31. 31.Find the value of x² − 2xy + y² when x = 8 and y = 4.
32. 32.If a − b = 5 and ab = 14, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 36² − 1².
34. 34.Use (a − b)² = a² − 2ab + b² to find 87².
35. 35.Use (a + b)² = a² + 2ab + b² to find 57².
36. 36.Use (a − b)² = a² − 2ab + b² to find 29².
37. 37.Use (a + b)(a − b) = a² − b² to find 66 × 54.
38. 38.Find the value of x² − y² when x = 14 and y = 6.
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 4.
40. 40.Use (a + b)² = a² + 2ab + b² to find 17².

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