Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 8 · 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 91 × 89.
2. 2.Use (a − b)² = a² − 2ab + b² to find 79².
3. 3.If a + b = 4 and ab = 3, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 46².
5. 5.Use a² − b² = (a + b)(a − b) to find 39² − 3².
6. 6.Find the value of x² + 2xy + y² when x = 11 and y = 6.
7. 7.Use a² − b² = (a + b)(a − b) to find 52² − 20².
8. 8.Use a² − b² = (a + b)(a − b) to find 28² − 16².
9. 9.Use (a + b)(a − b) = a² − b² to find 106 × 94.
10. 10.Use (a − b)² = a² − 2ab + b² to find 98².
11. 11.Use (a + b)(a − b) = a² − b² to find 59 × 41.
12. 12.If a − b = 1 and ab = 2, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 4.
14. 14.Find the value of x² − 2xy + y² when x = 15 and y = 8.
15. 15.Use (a − b)² = a² − 2ab + b² to find 52².
16. 16.Use (a − b)² = a² − 2ab + b² to find 25².
17. 17.Use a² − b² = (a + b)(a − b) to find 82² − 37².
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.If a + b = 11 and ab = 28, what is a² + b²?
20. 20.Find the value of x² − y² when x = 4 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 28² − 19².
22. 22.Use (a + b)(a − b) = a² − b² to find 69 × 51.
23. 23.Use a² − b² = (a + b)(a − b) to find 95² − 82².
24. 24.Use (a + b)² = a² + 2ab + b² to find 32².
25. 25.Use (a − b)² = a² − 2ab + b² to find 41².
26. 26.Use (a + b)(a − b) = a² − b² to find 48 × 32.
27. 27.Use (a − b)² = a² − 2ab + b² to find 54².
28. 28.Find the value of x² − 2xy + y² when x = 12 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 92².
30. 30.If a − b = 3 and ab = 28, what is a² + b²?
31. 31.If a − b = 6 and ab = 72, what is a² + b²?
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 38².
34. 34.Use (a + b)(a − b) = a² − b² to find 34 × 26.
35. 35.Use (a − b)² = a² − 2ab + b² to find 84².
36. 36.Use (a + b)(a − b) = a² − b² to find 103 × 97.
37. 37.Use (a + b)² = a² + 2ab + b² to find 26².
38. 38.Use (a − b)² = a² − 2ab + b² to find 32².
39. 39.Find the value of x² − 2xy + y² when x = 10 and y = 7.
40. 40.Use (a + b)² = a² + 2ab + b² to find 91².

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