因式分解/乘法展開

Geogebra 因式分解指令

1. Factors  over polynomial, number
2. Factor   over polynomial
3. IFactor  over irrational
4. CIFactor  over complex irrational

• Factors Command

Factors( <Polynomial> ) yields {factor, exponent}

Factors(x^3-1) yields {{x-1,1},{x^2+x+1,1}}

Factors( <Number> ) 

Gives matrix of the type  

(prime_1,exponent_1) 

(prime_2,exponent_2) 

......

Factors(1024) yields (2   10)

• Factor Command

Factor( <Polynomial> )   Factors the polynomial.

Factors(x^3-1) yields (x-1)(x^2+x+1)

• IFactor Command

Factors over irrationals

• CIFactor Command

Factors over complex irrationals.

https://wiki.geogebra.org/en/Algebra_Commands

Factors(1024)

Factors(59049)

Factors(1048576)

Factor(x^2-1)

Factor(x^3-1)

Factor(x^4-1)

Factor(x^2+2xy+y^2)

Factor(a^2+2ab+b^2) 會發生錯誤，因為Geogebra 將a,b 視為常數

Factor(x^3+3x^2 y+3x y^2+y^3)

Factor(x^4+4x^3 y+6x^2 y^2+4x y^3+y^4)

Pascal's Triangle

   

         1

       1  1

    1  2  1

  1 3   3  1

1 4   6  4 1

Geogebra 乘法展開指令

Expand((x^2-1)^2) yields x^2-2x+1