Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 980 · 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 = 13 and y = 10.
2. 2.Use (a + b)(a − b) = a² − b² to find 74 × 66.
3. 3.Use (a − b)² = a² − 2ab + b² to find 65².
4. 4.Use (a − b)² = a² − 2ab + b² to find 37².
5. 5.If a + b = 11 and ab = 18, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 88².
7. 7.Use (a − b)² = a² − 2ab + b² to find 72².
8. 8.Use (a − b)² = a² − 2ab + b² to find 16².
9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 31².
11. 11.Use (a + b)² = a² + 2ab + b² to find 86².
12. 12.Use (a + b)(a − b) = a² − b² to find 109 × 91.
13. 13.Use (a + b)² = a² + 2ab + b² to find 55².
14. 14.Use a² − b² = (a + b)(a − b) to find 66² − 39².
15. 15.Find the value of x² − 2xy + y² when x = 13 and y = 3.
16. 16.Use (a + b)(a − b) = a² − b² to find 23 × 17.
17. 17.Use (a − b)² = a² − 2ab + b² to find 42².
18. 18.Use (a − b)² = a² − 2ab + b² to find 29².
19. 19.Use (a + b)² = a² + 2ab + b² to find 106².
20. 20.Use (a + b)² = a² + 2ab + b² to find 74².
21. 21.Use (a + b)² = a² + 2ab + b² to find 41².
22. 22.If a + b = 4 and ab = 3, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 97².
24. 24.If a − b = 7 and ab = 44, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 36².
26. 26.If a + b = 7 and ab = 10, what is a² + b²?
27. 27.If a − b = 1 and ab = 6, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 75².
29. 29.Find the value of x² − y² when x = 7 and y = 1.
30. 30.Find the value of x² − y² when x = 6 and y = 3.
31. 31.If a + b = 19 and ab = 90, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 74².
33. 33.Use (a + b)(a − b) = a² − b² to find 71 × 69.
34. 34.Use (a + b)² = a² + 2ab + b² to find 61².
35. 35.Use a² − b² = (a + b)(a − b) to find 92² − 29².
36. 36.Use a² − b² = (a + b)(a − b) to find 71² − 65².
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 2.
38. 38.If a − b = 3 and ab = 28, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 89 × 71.
40. 40.Use (a + b)² = a² + 2ab + b² to find 103².

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