Question

All formulas of algebraic identities

CLASS 9​

Answer 1

Answer:

Given below are the algebraic identities which are considered very important maths formulas for Class 9.

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

(a + b) (a – b) = a2 -b2

(x + a) (x + b) = x2 + (a + b) x + ab

(x + a) (x – b) = x2 + (a – b) x – ab

(x – a) (x + b) = x2 + (b – a) x – ab

(x – a) (x – b) = x2 – (a + b) x + ab

(a + b)3 = a3 + b3 + 3ab (a + b)

(a – b)3 = a3 – b3 – 3ab (a – b)

(x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz

(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz

(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz

(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz

x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)

x2 + y2 = \(\frac{1}{2}\) [(x + y)2 + (x – y)2]

(x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc

x3 + y3 = (x + y) (x2 – xy + y2)

x3 – y3 = (x – y) (x2 + xy + y2)

x2 + y2 + z2 – xy – yz – zx = \(\frac{1}{2}\) [(x – y)2 + (y – z)2 + (z – x)2]

Answer 2

Answer:

1. (a + b)2 = a2 + 2ab + b2

2. (a − b)2 = a2 − 2ab + b2

3. (a + b)(a – b) = a2 – b2

4. (x + a)(x + b) = x2 + (a + b)x + ab

5. (x + a)(x – b) = x2 + (a – b)x – ab

6. (x – a)(x + b) = x2 + (b – a)x – ab

7. (x–a)(x–b) = x2 – (a+b)x + ab

8. (a + b)3 = a3 + b3 + 3ab(a + b)

9. (a – b)3 = a3 – b3 – 3ab(a – b)

10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz

11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz

12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz

13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz

14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz − xz)

15. x2 + y2 = 12[(x + y)2 + (x – y)2]

16. (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc

17. x3 + y3 = (x + y)(x2 – xy + y2)

18. x3 – y3 = (x – y)(x2 + xy + y2)

19. x2 + y2 + z2 − xy – yz –zx = 1/2[(x − y)2 + (y − z)2 + (z − x)2]

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