Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 322 · 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 + 2xy + y² when x = 6 and y = 3.
2. 2.Use (a + b)² = a² + 2ab + b² to find 44².
3. 3.Use (a + b)(a − b) = a² − b² to find 78 × 62.
4. 4.Use a² − b² = (a + b)(a − b) to find 72² − 4².
5. 5.If a − b = 5 and ab = 14, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 62².
7. 7.Use (a + b)(a − b) = a² − b² to find 74 × 66.
8. 8.Use (a − b)² = a² − 2ab + b² to find 16².
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 2.
10. 10.Use a² − b² = (a + b)(a − b) to find 76² − 15².
11. 11.If a − b = 2 and ab = 63, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 8 and y = 7.
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 2.
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.Use (a + b)² = a² + 2ab + b² to find 61².
16. 16.Use (a + b)(a − b) = a² − b² to find 34 × 26.
17. 17.Use a² − b² = (a + b)(a − b) to find 65² − 32².
18. 18.Find the value of x² + 2xy + y² when x = 5 and y = 3.
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.If a + b = 4 and ab = 3, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 68².
22. 22.Use a² − b² = (a + b)(a − b) to find 35² − 4².
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Use a² − b² = (a + b)(a − b) to find 47² − 14².
25. 25.Use (a − b)² = a² − 2ab + b² to find 78².
26. 26.Use (a + b)(a − b) = a² − b² to find 56 × 44.
27. 27.Use (a + b)(a − b) = a² − b² to find 36 × 24.
28. 28.Use (a + b)² = a² + 2ab + b² to find 31².
29. 29.Use (a − b)² = a² − 2ab + b² to find 46².
30. 30.Use (a − b)² = a² − 2ab + b² to find 99².
31. 31.Use a² − b² = (a + b)(a − b) to find 75² − 7².
32. 32.Use a² − b² = (a + b)(a − b) to find 92² − 65².
33. 33.Use (a − b)² = a² − 2ab + b² to find 92².
34. 34.Use (a + b)² = a² + 2ab + b² to find 86².
35. 35.Use (a + b)² = a² + 2ab + b² to find 78².
36. 36.Use (a − b)² = a² − 2ab + b² to find 27².
37. 37.Use (a + b)(a − b) = a² − b² to find 49 × 31.
38. 38.If a − b = 5 and ab = 66, what is a² + b²?
39. 39.If a − b = 7 and ab = 60, what is a² + b²?
40. 40.If a + b = 20 and ab = 99, what is a² + b²?

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