 # Some Useful Algebra Formulas

Just remembering Algebra (math) formulas are not going to help you to crack any examinations, one should have the ability to execute these formulas in the exam hall. To do that, one has to practice the various types of algebraic math problems repeatedly.

## Some Important Formulas of Algebra

### Square Formula

• `01` (x+y)= (x+y)(x+y) = x2+2xy+y2
• `02` (x-y)= (x-y)(x-y) = x2-2xy+y2
• `03` (x+y)= (x-y)2 + 4xy
• `04` (x-y)= (x+y)2 – 4xy
• `05` x2-y2 = (x+y)(x+y)
• `06` (x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yx
• `07` 4xy = [ (x+y)2 – (x-y)2 ]
• `08` 2( x2+y2) = [ (x+y)2 + (x-y)2 ]

### Cube Formula

• `01` (x + y)3 = x3 + 3x2y + 3xy2 + y3
• `02`  (x + y)3 = x3 + y3 + 3xy(x + y)
• `03`  (x – y)3 = x3 – 3x2y + 3xy2 – y3
• `04`  (x – y)3 = x3 – y3 – 3xy(x – y)
• `05`  x3 + y3 = (x + y)(y2 – xy + y2)
• `06`  x3 – y3 = (x – y)(x2 + xy + y2)
• `07`  (x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4)
• `08`  (x – y)4 = x4 – 4x3y + 6x2y2 – 4xy3 + y4)
• `09`  x4 – y4 = (x2 + y2)(x + y) (x – y)
• `10`  x3 + y3 + z3 – 3xyz = (x + y + z)( x2 + y2 + z2 -xy – yz – zx)

### Laws of Exponent

• `01`  xm × xn = xm+n
• `02`  xm / xn = xm-n
• `03`  (xy)m = xm × ym
• `04`  (xm)n = xmn
• `05`  xm = (1/x-m)
• `06`  x0 = 1
• `07` √x = x½
• `08` ³√x = x¹/³

`01` If a Quadratic Equation is ax2 + bx + c = 0 ; Then the roots of this equation are –