Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 986 · 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.Find the value of x² − y² when x = 12 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 29 × 11.
3. 3.If a − b = 10 and ab = 11, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 75².
5. 5.Use (a − b)² = a² − 2ab + b² to find 87².
6. 6.Use (a + b)² = a² + 2ab + b² to find 33².
7. 7.If a − b = 1 and ab = 12, what is a² + b²?
8. 8.If a − b = 5 and ab = 66, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 14².
10. 10.Find the value of x² − y² when x = 12 and y = 7.
11. 11.Find the value of x² − 2xy + y² when x = 12 and y = 11.
12. 12.Use (a + b)(a − b) = a² − b² to find 44 × 36.
13. 13.Use a² − b² = (a + b)(a − b) to find 98² − 95².
14. 14.Use a² − b² = (a + b)(a − b) to find 44² − 9².
15. 15.Use (a + b)² = a² + 2ab + b² to find 48².
16. 16.Find the value of x² − y² when x = 6 and y = 4.
17. 17.Use (a + b)² = a² + 2ab + b² to find 69².
18. 18.Find the value of x² + 2xy + y² when x = 10 and y = 3.
19. 19.Use a² − b² = (a + b)(a − b) to find 94² − 75².
20. 20.Use (a + b)(a − b) = a² − b² to find 107 × 93.
21. 21.Use (a + b)(a − b) = a² − b² to find 78 × 62.
22. 22.Use (a − b)² = a² − 2ab + b² to find 46².
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 53² − 26².
25. 25.Find the value of x² + 2xy + y² when x = 15 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 13 and y = 6.
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Use (a + b)(a − b) = a² − b² to find 53 × 47.
29. 29.Use (a + b)² = a² + 2ab + b² to find 13².
30. 30.Use (a + b)(a − b) = a² − b² to find 34 × 26.
31. 31.Find the value of x² − 2xy + y² when x = 3 and y = 2.
32. 32.Use (a + b)(a − b) = a² − b² to find 67 × 53.
33. 33.Use (a − b)² = a² − 2ab + b² to find 67².
34. 34.Use (a − b)² = a² − 2ab + b² to find 72².
35. 35.Find the value of x² − 2xy + y² when x = 12 and y = 10.
36. 36.If a + b = 5 and ab = 6, what is a² + b²?
37. 37.Find the value of x² − 2xy + y² when x = 13 and y = 7.
38. 38.Use (a − b)² = a² − 2ab + b² to find 29².
39. 39.Use (a + b)² = a² + 2ab + b² to find 54².
40. 40.Use (a + b)² = a² + 2ab + b² to find 47².

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