Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 977 · 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 33 × 27.
2. 2.Use (a − b)² = a² − 2ab + b² to find 14².
3. 3.Use a² − b² = (a + b)(a − b) to find 36² − 13².
4. 4.Use (a + b)(a − b) = a² − b² to find 34 × 26.
5. 5.Use (a − b)² = a² − 2ab + b² to find 97².
6. 6.Use (a + b)(a − b) = a² − b² to find 48 × 32.
7. 7.Use (a + b)(a − b) = a² − b² to find 67 × 53.
8. 8.If a − b = 9 and ab = 36, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 79 × 61.
10. 10.Use (a − b)² = a² − 2ab + b² to find 49².
11. 11.Use (a + b)² = a² + 2ab + b² to find 76².
12. 12.Use (a + b)² = a² + 2ab + b² to find 48².
13. 13.Use (a − b)² = a² − 2ab + b² to find 12².
14. 14.Find the value of x² − y² when x = 15 and y = 12.
15. 15.If a − b = 5 and ab = 36, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 39².
17. 17.Find the value of x² − y² when x = 4 and y = 3.
18. 18.Use (a + b)² = a² + 2ab + b² to find 89².
19. 19.Find the value of x² + 2xy + y² when x = 6 and y = 1.
20. 20.Use (a + b)(a − b) = a² − b² to find 101 × 99.
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 1.
22. 22.Use (a + b)(a − b) = a² − b² to find 56 × 44.
23. 23.Use a² − b² = (a + b)(a − b) to find 30² − 21².
24. 24.Use (a + b)² = a² + 2ab + b² to find 99².
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 5.
26. 26.If a − b = 2 and ab = 80, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 39².
28. 28.Use (a − b)² = a² − 2ab + b² to find 67².
29. 29.Use (a + b)² = a² + 2ab + b² to find 13².
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 4.
31. 31.Find the value of x² − 2xy + y² when x = 13 and y = 7.
32. 32.Use a² − b² = (a + b)(a − b) to find 35² − 29².
33. 33.Use (a + b)(a − b) = a² − b² to find 43 × 37.
34. 34.Use (a + b)(a − b) = a² − b² to find 89 × 71.
35. 35.Use (a − b)² = a² − 2ab + b² to find 38².
36. 36.Use (a − b)² = a² − 2ab + b² to find 33².
37. 37.Use a² − b² = (a + b)(a − b) to find 53² − 48².
38. 38.Use (a + b)² = a² + 2ab + b² to find 26².
39. 39.Use (a − b)² = a² − 2ab + b² to find 37².
40. 40.Use (a − b)² = a² − 2ab + b² to find 85².

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