Inicio › Matemáticas 3 › Factorización

Matemáticas 3 · Tema 12

Factorización

Ejemplos

8x2y3−6y3x5−10y3a2x48x^2y^3 - 6y^3x^5 - 10y^3a^2x^4

Factor común

(2x2y3)(4−3x3−5x2a2)(2x^2y^3)(4 - 3x^3 - 5x^2a^2)
25y6a4−16x825y^6a^4 - 16x^8

Diferencia de cuadrados

(5y3a2−4x4)(5y3a2+4x4)(5y^3a^2 - 4x^4)(5y^3a^2 + 4x^4)
x2−10x+25=(x−5)(x−5)x^2 - 10x + 25 = (x - 5)(x - 5)

Trinomio cuadrado perfecto

(x−5)2(x - 5)^2
(−5)(−5)=25(-5)(-5) = 25
−5−5=−10-5 - 5 = -10
x2−8x−9x^2 - 8x - 9

Trinomio

(x+1)(x−9)(x + 1)(x - 9)
(1)(−9)=−9(1)(-9) = -9
1−9=−81 - 9 = -8

Ejercicios

Bloque 1
10x4y2−5x3y3−20x4=10x^4y^2 - 5x^3y^3 - 20x^4 =
36x8a4−100x6=36x^8a^4 - 100x^6 =
x2+6x+9=x^2 + 6x + 9 =
x2−3x−10=x^2 - 3x - 10 =
Bloque 2
12x5y3−4x3y2−20x7=12x^5y^3 - 4x^3y^2 - 20x^7 =
25x6a2−49x8=25x^6a^2 - 49x^8 =
x2−8x+16=x^2 - 8x + 16 =
x2−2x−8=x^2 - 2x - 8 =
Bloque 3
14x7y2−7x5y3+14y5=14x^7y^2 - 7x^5y^3 + 14y^5 =
25x8a4−36x6=25x^8a^4 - 36x^6 =
x2−2x+1=x^2 - 2x + 1 =
x2+x−20=x^2 + x - 20 =
Bloque 4
20x5y3−4x2y4+8x3=20x^5y^3 - 4x^2y^4 + 8x^3 =
100x6a2−25x8=100x^6a^2 - 25x^8 =
x2−12x+36=x^2 - 12x + 36 =
x2+6x+8=x^2 + 6x + 8 =

Respuestas

▼

Bloque 1

10x4y2−5x3y3−20x410x^4y^2 - 5x^3y^3 - 20x^4
(5x3)(2xy2−y3−4x)(5x^3)(2xy^2 - y^3 - 4x)
36x8a4−100x636x^8a^4 - 100x^6
(6x4a2−10x3)(6x4a2+10x3)(6x^4a^2 - 10x^3)(6x^4a^2 + 10x^3)
x2+6x+9=(x+3)(x+3)x^2 + 6x + 9 = (x + 3)(x + 3)
(x+3)2(x + 3)^2
(3)(3)=9(3)(3) = 9
3+3=63 + 3 = 6
x2−3x−10x^2 - 3x - 10
(x+2)(x−5)(x + 2)(x - 5)
(2)(−5)=−10(2)(-5) = -10
2−5=−32 - 5 = -3

Bloque 2

12x5y3−4x3y2−20x712x^5y^3 - 4x^3y^2 - 20x^7
(4x3)(3x2y3−y2−5x4)(4x^3)(3x^2y^3 - y^2 - 5x^4)
25x6a2−49x825x^6a^2 - 49x^8
(5x3a−7x4)(5x3a+7x4)(5x^3a - 7x^4)(5x^3a + 7x^4)
x2−8x+16=(x−4)(x−4)x^2 - 8x + 16 = (x - 4)(x - 4)
(x−4)2(x - 4)^2
(−4)(−4)=16(-4)(-4) = 16
−4−4=−8-4 - 4 = -8
x2−2x−8x^2 - 2x - 8
(x+2)(x−4)(x + 2)(x - 4)
(2)(−4)=−8(2)(-4) = -8
2−4=−22 - 4 = -2

Bloque 3

14x7y2−7x5y3+14y514x^7y^2 - 7x^5y^3 + 14y^5
(7y2)(2x7−x5y+2y3)(7y^2)(2x^7 - x^5y + 2y^3)
25x8a4−36x625x^8a^4 - 36x^6
(5x4a2−6x3)(5x4a2+6x3)(5x^4a^2 - 6x^3)(5x^4a^2 + 6x^3)
x2−2x+1=(x−1)(x−1)x^2 - 2x + 1 = (x - 1)(x - 1)
(x−1)2(x - 1)^2
(−1)(−1)=1(-1)(-1) = 1
−1−1=−2-1 - 1 = -2
x2+x−20x^2 + x - 20
(x+5)(x−4)(x + 5)(x - 4)
(5)(−4)=−20(5)(-4) = -20
5−4=15 - 4 = 1

Bloque 4

20x5y3−4x2y4+8x320x^5y^3 - 4x^2y^4 + 8x^3
(4x2)(5x3y3−y4+2x)(4x^2)(5x^3y^3 - y^4 + 2x)
100x6a2−25x8100x^6a^2 - 25x^8
(10x3a−5x4)(10x3a+5x4)(10x^3a - 5x^4)(10x^3a + 5x^4)
x2−12x+36=(x−6)(x−6)x^2 - 12x + 36 = (x - 6)(x - 6)
(x−6)2(x - 6)^2
(−6)(−6)=36(-6)(-6) = 36
−6−6=−12-6 - 6 = -12
x2+6x+8x^2 + 6x + 8
(x+4)(x+2)(x + 4)(x + 2)
(4)(2)=8(4)(2) = 8
4+2=64 + 2 = 6

Ejercicios extra

▼
Bloque 1
18x4y2−12x3y3+6x2y=18x^4y^2 - 12x^3y^3 + 6x^2y =
49x6y4−64x2=49x^6y^4 - 64x^2 =
x2+10x+25=x^2 + 10x + 25 =
x2−5x−14=x^2 - 5x - 14 =
15x3y5−25x2y4−5xy3=15x^3y^5 - 25x^2y^4 - 5xy^3 =
Bloque 2
81x4a6−16y8=81x^4a^6 - 16y^8 =
x2−14x+49=x^2 - 14x + 49 =
x2+3x−18=x^2 + 3x - 18 =
24x6y2−8x4y3+16x2y=24x^6y^2 - 8x^4y^3 + 16x^2y =
x2−7x+12=x^2 - 7x + 12 =
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