Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 32 · 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 69 × 51.
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 2.
3. 3.Use (a + b)² = a² + 2ab + b² to find 92².
4. 4.If a − b = 2 and ab = 24, what is a² + b²?
5. 5.If a + b = 5 and ab = 4, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 73 × 67.
7. 7.Use (a + b)(a − b) = a² − b² to find 22 × 18.
8. 8.Use (a + b)(a − b) = a² − b² to find 25 × 15.
9. 9.Use a² − b² = (a + b)(a − b) to find 55² − 6².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Use (a + b)(a − b) = a² − b² to find 64 × 56.
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 24².
13. 13.Use (a − b)² = a² − 2ab + b² to find 79².
14. 14.Use a² − b² = (a + b)(a − b) to find 78² − 12².
15. 15.If a − b = 3 and ab = 88, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 104².
17. 17.Use a² − b² = (a + b)(a − b) to find 77² − 57².
18. 18.Use (a + b)² = a² + 2ab + b² to find 46².
19. 19.Use a² − b² = (a + b)(a − b) to find 40² − 37².
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 25².
22. 22.Find the value of x² − y² when x = 15 and y = 6.
23. 23.Use (a + b)² = a² + 2ab + b² to find 36².
24. 24.Use (a + b)² = a² + 2ab + b² to find 12².
25. 25.If a − b = 3 and ab = 28, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 66² − 25².
27. 27.Use a² − b² = (a + b)(a − b) to find 22² − 12².
28. 28.If a + b = 4 and ab = 3, what is a² + b²?
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 24 × 16.
31. 31.Find the value of x² + 2xy + y² when x = 14 and y = 7.
32. 32.Use (a + b)² = a² + 2ab + b² to find 85².
33. 33.Use (a − b)² = a² − 2ab + b² to find 57².
34. 34.Use a² − b² = (a + b)(a − b) to find 89² − 2².
35. 35.Use (a + b)² = a² + 2ab + b² to find 21².
36. 36.Use a² − b² = (a + b)(a − b) to find 43² − 21².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 107 × 93.
39. 39.Use (a + b)² = a² + 2ab + b² to find 101².
40. 40.Use (a + b)(a − b) = a² − b² to find 32 × 28.

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