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# EJERCICIOS PARA EL EXAMEN

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### EJERCICIOS PARA EL EXAMEN

1. 1. 1. PRODUCTO DE DOS BINOMIOS DE LA FORMA (x+a) (x+b) a) (ax+1 - 6) (ax+1 - 5) =a2x+2 + 30 - 6a x+1 - 5a x+1 =a2x+2 - 11a x+1 + 30 2. EL CUADRADO DE UN MULTINOMIO b) (2x3 - x2 + 4x - 3)2 = (2x3)2 + (-x2)2 + (4x)2 + (-3)2 + 2(2x3) (-x2) + 2(2x3) (4x) + 2(2x3) (-3) + 2(-x2) (4x) + 2(-x2) (-3) + 2(4x) (-3) = 4x6 + x4 +16x2 + 9 – 4x5 +16x4 -12x3 – 8x3 + 6x2 -24x = 4x6 - 4x5 +17x4 - 20x3 + 22x2 – 24x +9 3. FACTORAR O DESCOMPONER EN DOS FACTORES c) 24a2xy2 - 36x2y4 =6xy2 (4a2 -6xy2) d) (a+3) (a+1) – 4 (a+1) (a + 3) (a + 1) = (a + 3) 4(a + 1) = -4 (a + 1) (a + 1)
2. 2. = (a + 1) (a + 3 – 4) = (a + 1) (a – 1) e) a2b3 – n4 + a2b3x2 – n4x2 – 3a2b3x + 3n4x = ( a2b3 + a2b3x2 – 3a2b3x) (– n4 – n4x2 + 3n4x) = a2b3 (1 + x2 - 3x) – n4 (1 + x2 – 3x) = (1 + x2 - 3x) (a2b3 – n4 ) 4. FACTORAR UN TRINOMIO CUADRADO PERFECTO f) 1 + 25x4 - x2 25 36 3 = 25x4 - x2 + 1 36 3 25 = (5 x2 - 1)2 6 5 5. DIFERENCIA DE CUADRADOS g) x2 - y2z4 100 81
3. 3. =( x + yz2) (x - yz2) 10 9 10 9 6. TRINOMIO CUADRADO PERFECTO POR ADICIÓN Y SUSTRACCIÓN h) 81m8 + 2m4 + 1 = 81m8 + 2m4 + 1 16m4 - 16m4 81m8 +18m4 + 1 - 16m4 = (9m4 + 1)2 - 16m4 = (9m4 + 1 - 4m2) (9m4 + 1 + 4m2) = (9m4 - 4m2 + 1) (9m4 + 4m2 + 1) 7. TRINOMIO DE LA FORMA x2 + bx + c y ax2 + bx + c i) m2 - 2m - 168 = (m – 14) (m + 12) j) 20n2 - 9n – 20 = 20(20n2) – 20(9n) – 20(20)
4. 4. = 400n2 – 20(9n) – 400 = 20n2 – 25) (20n + 16) 20 = 20n2 – 25) (20n + 16) 5 4 = (4n – 5) (5n + 4) 8. CUBO PERFECTO DE BINOMIOS k) 125x3 + 1 +75x2 + 15x = 125x3 + 75x2 + 15x + 1 3(5x)2 (1)= 75x2 3(5x) (1)2 = 15x = (5x + 1 )3 9. SUMA O DIFERENCIA DE CUBOS PERFECTOS l) 27a3 – b3 = (3a - b) (3a) 2+ (3a) (b) + (b)2 = (3a – b) (9a2 + 3ab +b2)