Question

List the algebraic formulas for class 9

Answer 1

Algebraic Formulas

Some algebraic formulas for class 9th are as follows :-

• (a+b)² = a² + b² + 2ab

• (a-b)² = a² + b² - 2ab

• (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 + 2zx

• (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)(x²+y²+z²-xy-yz-zx) = x³ + y³ + z³ -3xyz

• (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)

Answer 2

some formulas used in algebra ..

Step-by-step explanation:

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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