Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 424 · 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 36².
2. 2.If a − b = 1 and ab = 6, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 3 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 24².
5. 5.Find the value of x² − 2xy + y² when x = 4 and y = 1.
6. 6.Use (a + b)(a − b) = a² − b² to find 35 × 25.
7. 7.Use (a − b)² = a² − 2ab + b² to find 57².
8. 8.If a − b = 1 and ab = 110, what is a² + b²?
9. 9.If a − b = 3 and ab = 18, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 72² − 20².
11. 11.Find the value of x² − y² when x = 6 and y = 3.
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.Use (a + b)² = a² + 2ab + b² to find 87².
14. 14.If a − b = 5 and ab = 66, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 102 × 98.
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 9².
17. 17.Use (a + b)(a − b) = a² − b² to find 22 × 18.
18. 18.Use a² − b² = (a + b)(a − b) to find 94² − 37².
19. 19.Use a² − b² = (a + b)(a − b) to find 29² − 9².
20. 20.Use (a + b)² = a² + 2ab + b² to find 44².
21. 21.Use (a − b)² = a² − 2ab + b² to find 52².
22. 22.Use (a + b)² = a² + 2ab + b² to find 67².
23. 23.Use (a + b)² = a² + 2ab + b² to find 104².
24. 24.Use (a + b)(a − b) = a² − b² to find 72 × 68.
25. 25.If a + b = 16 and ab = 60, what is a² + b²?
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 86².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.Use (a − b)² = a² − 2ab + b² to find 47².
30. 30.Find the value of x² − 2xy + y² when x = 6 and y = 4.
31. 31.Find the value of x² + 2xy + y² when x = 8 and y = 5.
32. 32.Use (a − b)² = a² − 2ab + b² to find 29².
33. 33.Use (a − b)² = a² − 2ab + b² to find 45².
34. 34.Use (a + b)(a − b) = a² − b² to find 95 × 85.
35. 35.Use (a − b)² = a² − 2ab + b² to find 32².
36. 36.Use a² − b² = (a + b)(a − b) to find 75² − 6².
37. 37.If a − b = 1 and ab = 2, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 93 × 87.
39. 39.Use (a + b)(a − b) = a² − b² to find 81 × 79.
40. 40.Use a² − b² = (a + b)(a − b) to find 91² − 24².

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