Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 320 · 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 = 7 and y = 1.
2. 2.Use (a + b)² = a² + 2ab + b² to find 35².
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 78².
5. 5.If a − b = 5 and ab = 84, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 68 × 52.
7. 7.Use (a + b)(a − b) = a² − b² to find 37 × 23.
8. 8.Use (a − b)² = a² − 2ab + b² to find 84².
9. 9.Use (a − b)² = a² − 2ab + b² to find 92².
10. 10.Use (a − b)² = a² − 2ab + b² to find 79².
11. 11.Find the value of x² − 2xy + y² when x = 9 and y = 2.
12. 12.Use (a − b)² = a² − 2ab + b² to find 44².
13. 13.Use (a − b)² = a² − 2ab + b² to find 61².
14. 14.Use (a − b)² = a² − 2ab + b² to find 25².
15. 15.Use (a − b)² = a² − 2ab + b² to find 35².
16. 16.Use (a + b)(a − b) = a² − b² to find 52 × 48.
17. 17.Use (a + b)(a − b) = a² − b² to find 58 × 42.
18. 18.Use a² − b² = (a + b)(a − b) to find 72² − 10².
19. 19.Use (a + b)(a − b) = a² − b² to find 53 × 47.
20. 20.Use (a + b)² = a² + 2ab + b² to find 19².
21. 21.Use a² − b² = (a + b)(a − b) to find 74² − 33².
22. 22.Use (a − b)² = a² − 2ab + b² to find 94².
23. 23.Use (a + b)(a − b) = a² − b² to find 108 × 92.
24. 24.Use (a − b)² = a² − 2ab + b² to find 48².
25. 25.If a + b = 6 and ab = 8, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 39 × 21.
27. 27.Use a² − b² = (a + b)(a − b) to find 37² − 24².
28. 28.Use (a + b)(a − b) = a² − b² to find 55 × 45.
29. 29.Use (a + b)² = a² + 2ab + b² to find 32².
30. 30.Use (a + b)(a − b) = a² − b² to find 93 × 87.
31. 31.Use (a − b)² = a² − 2ab + b² to find 15².
32. 32.If a − b = 8 and ab = 20, what is a² + b²?
33. 33.If a + b = 18 and ab = 80, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 12 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 33².
36. 36.If a − b = 3 and ab = 18, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 18².
38. 38.Use a² − b² = (a + b)(a − b) to find 21² − 3².
39. 39.Use a² − b² = (a + b)(a − b) to find 41² − 38².
40. 40.Use a² − b² = (a + b)(a − b) to find 65² − 63².

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