Browse By

Calendar

November 2024
M T W T F S S
 123
45678910
11121314151617
18192021222324
252627282930  

JEE Main – Algebraic Formulas Notes

by admin in Notes
  • Algebra Formulas: It is an important field of study in Mathematics.
  • In this case, we generally use symbols and letters to represent quantities and numbers in equations and formulae.
  • Algebra in many chapters like the algebra of real numbers, algebra of complex numbers, algebra of derivative of a function, and algebra of event.
  • Many algebraic formulas are difficult to remember. It is included in this article.

Algebraic Formulas

What is Algebra?

The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

For Example: (X-1)(Y+2)

Term: A word or phrase used to describe a thing or to express a concept Expression: It is a mathematical sentence; it doesn’t have an equal sign Equation: It is a complete Mathematical sentence that includes a sign of equality

Algebraic Expression

  •  A number or a combination of numbers connected by the symbols of operation +,-,*,/ is called an algebraic expression.
  • E.g.- 3x, 2x, -3/5x
  • If a and b are two integers, the following are basic algebraic expressions:
    • Addition equation: a + b
    • Subtraction equation: b – a
    • Multiplication equation: ab
    • Division equation: a/b or a ÷ b

List Of Important Algebra Formulas

The basic algebraic formulas are:

Square Formulas

  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. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
  9. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  10. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  11. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  12. x2+y2=1/2[(x+y)2+(x–y)2]
  13. x2+y2+z2−xy–yz–zx=1/2[(x−y)2+(y−z)2+(z−x)2]

Cube Formulas

  1. (a + b)3 = a3 + b3 + 3ab (a + b)
  2. (a – b)3 = a3 – b3 – 3ab (a – b)
  3. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
  4. a3 + b3 = (a + b) (a2 – ab + b2)
  5. a3 – b3 = (a – b) (a2 + ab + b2)
  6. (x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc
  7. if (a+b+c) = 0, a3 + b3 + c3 – 3abc

Other Formula

  1. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  2. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  3. a4 – b4 = (a2 – b2)(a2 + b2)
  4. a5 – b5 = (a – b)(a4+ a3b + a2b2 + ab3 + b4 )
  5. a5 + b5 = (a + b)(a4  – a3b + a2b2– ab3 + b4 )

Power n formula

  • If n is even, then: an – bn = (a – b)(an-1 + an-2b +an-3b2 + …+ abn-2 + bn-1)
  • If n is odd, then: an + bn = (a + b)(an-1 – an-2b  +an-3b2 – …- abn-2 + bn-1)

Exponent Formula

  • (am )(an ) = am+n 
  • (ab)m = ambm
  • (am)n = amn

Fraction Exponent

Cyclic Factor

If an expression remain same after replacing a by b, b by c, c by a, then it is called cyclic expression and its factor are called cyclic factor.

All the important algebra formulas for class 8 to class 11 are listed above. It is easy for students to learn this formula. This formula will help you in competitive or board exams.

Recommended Reading

References

teachoo

Tagged with: