10 ejercicios de factorizacion
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1) 14x2 y2 - 28x3 + 56x4R: 14x2 (y2 - 2x + 4x2)
2) X3 + x5 – x7 = R: x3 (1 + x2 - x4)
3) 100a2 b3c –150ab2c2 + 50 ab3c3 - 200abc2=R: 50abc (2ab2 – 3bc +b2c2 – 4c)
4) a(x + 1) + b(x + 1)R: (x + 1) (a +b)
5) (3x + 2) (x + y – z) – (3x + 2) - (x + y – 1)( 3x +2)
R: (3x + 2) (x + y – z) – (3x + 2)(1) – ( x - y +1)( 3x +2)
(3x + 2) (x + y – z -1 –x - y + 1)
-z ( 3x +2)
6) (a + b -1) (a 2 + 1) – a2 – 1
R: ( a + b -1) (a 2 + 1) –( a2 + 1)
( a2 + 1)(a + b - 1)-1
( a2 + 1)(a + b -1 -1)
( a2 + 1)(a + b -2)
7) a2 + ab + ax + bx(a2 + ab) + (ax + b)a(a + b) + x(a +b)(a + b) (a +x)
8) 4am3 – 12 amn – m2 + 3n= (4am3 – 12amn) – (m2 + 3n)=4am (m2 – 3n) – (m2 + 3n)R: (m2 – 3n)(4am-1)
9) a2b3 – n4 + a2b3x2 – n4x2 – 3a3b3x + 3n4x= (a2b3 – n4 + a2b3x2 – n4x2 – 3a3b3x + 3n4x)= (a2b3 + a2b3x2 – 3a2b3x) – (n4 + n4x2 - 3n4x)= a2b3 (1 + x2 – 3x)- n4 (1 + x2 -3x)R: (1 + x2 – 3x) (a2b3 - n4 )
10) a2 + 2a (a – b) + (a – b) 2
Raíz cuadrada de a2 = a
Raíz cuadrada de (a – b) 2 = (a – b)
Doble producto sus raíces
(2 X a X (a – b) = 2a(a – b) (cumple)
R: (a + (a – b)) 2
(a + a – b) = (2a –b) 2
2) X3 + x5 – x7 = R: x3 (1 + x2 - x4)
3) 100a2 b3c –150ab2c2 + 50 ab3c3 - 200abc2=R: 50abc (2ab2 – 3bc +b2c2 – 4c)
4) a(x + 1) + b(x + 1)R: (x + 1) (a +b)
5) (3x + 2) (x + y – z) – (3x + 2) - (x + y – 1)( 3x +2)
R: (3x + 2) (x + y – z) – (3x + 2)(1) – ( x - y +1)( 3x +2)
(3x + 2) (x + y – z -1 –x - y + 1)
-z ( 3x +2)
6) (a + b -1) (a 2 + 1) – a2 – 1
R: ( a + b -1) (a 2 + 1) –( a2 + 1)
( a2 + 1)(a + b - 1)-1
( a2 + 1)(a + b -1 -1)
( a2 + 1)(a + b -2)
7) a2 + ab + ax + bx(a2 + ab) + (ax + b)a(a + b) + x(a +b)(a + b) (a +x)
8) 4am3 – 12 amn – m2 + 3n= (4am3 – 12amn) – (m2 + 3n)=4am (m2 – 3n) – (m2 + 3n)R: (m2 – 3n)(4am-1)
9) a2b3 – n4 + a2b3x2 – n4x2 – 3a3b3x + 3n4x= (a2b3 – n4 + a2b3x2 – n4x2 – 3a3b3x + 3n4x)= (a2b3 + a2b3x2 – 3a2b3x) – (n4 + n4x2 - 3n4x)= a2b3 (1 + x2 – 3x)- n4 (1 + x2 -3x)R: (1 + x2 – 3x) (a2b3 - n4 )
10) a2 + 2a (a – b) + (a – b) 2
Raíz cuadrada de a2 = a
Raíz cuadrada de (a – b) 2 = (a – b)
Doble producto sus raíces
(2 X a X (a – b) = 2a(a – b) (cumple)
R: (a + (a – b)) 2
(a + a – b) = (2a –b) 2
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