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Factorización 1

Total questions: 20

Worksheet time: 31mins

Name
Class
Date
1.

 1−(x−2y)21-(x-2y)^2  

a)

 (1+x−2y)(1−x+2y)\left(1+x-2y\right)\left(1-x+2y\right)  

b)

 (1−x−2y)(1+x+2y)\left(1-x-2y\right)\left(1+x+2y\right)  

c)

 (1+x+2y)(1+x−2y)\left(1+x+2y\right)\left(1+x-2y\right)  

d)

 (1+x−y)(1−x+y)\left(1+x-y\right)\left(1-x+y\right)  

2.

 1−b+2a(1−b)1-b+2a(1-b)  

a)

 (1+b)(1+2a)\left(1+b\right)\left(1+2a\right)  

b)

 (1−b)(1+2a)\left(1-b\right)\left(1+2a\right)  

c)

 (1−b)(1−2a)\left(1-b\right)\left(1-2a\right)  

d)

 (1−b)(1+a)\left(1-b\right)\left(1+a\right)  

3.

 3m2−7x2y+3my−7mx23m^2-7x^2y+3my-7mx^2  

a)

 (m+y)(m−7x2)\left(m+y\right)\left(m-7x^2\right)  

b)

 (m+y)(3m−x2)\left(m+y\right)\left(3m-x^2\right)  

c)

 (m+y)(3m−7x2)\left(m+y\right)\left(3m-7x^2\right)  

d)

 (m+y)(3m+7x2)\left(m+y\right)\left(3m+7x^2\right)  

4.

 15m2n2−24mn6−36m3n215m^2n^2-24mn^6-36m^3n^2  

a)

 3mn2 (5m−8n4−2m2)3mn^2\ \left(5m-8n^4-2m^2\right)  

b)

 3mn (5m−8n4−12m2)3mn^{ }\ \left(5m-8n^4-12m^2\right)  

c)

 3m2n2 (5m−8n4−12m2)3m^2n^2\ \left(5m-8n^4-12m^2\right)  

d)

 3mn2 (5m−8n4−12m2)3mn^2\ \left(5m-8n^4-12m^2\right)  

5.

 6ax−3a−1+2x6ax-3a-1+2x  

a)

 (3a+1)(2x−1)\left(3a+1\right)\left(2x-1\right)  

b)

 (3a+1)(2x+1)\left(3a+1\right)\left(2x+1\right)  

c)

 (3a−1)(2x−1)\left(3a-1\right)\left(2x-1\right)  

d)

 (3a−1)(2x+1)\left(3a-1\right)\left(2x+1\right)  

6.

 4m3y+5x2m−8xmy+7x2m2y24m^3y+5x^2m-8xmy+7x^2m^2y^2  

a)

 m(4m2y+5x2−8xy+7x2my2)m\left(4m^2y+5x^2-8xy+7x^2my^2\right)  

b)

 m2(4m2y+5x2−8xy+7x2my2)m^2\left(4m^2y+5x^2-8xy+7x^2my^2\right)  

c)

 m(4m2y2+5x2−8xy+7x2my2)m\left(4m^2y^2+5x^2-8xy+7x^2my^2\right)  

d)

 m(4m2y+5x2−8xm+7x2my2)m\left(4m^2y+5x^2-8xm+7x^2my^2\right)  

7.

 2ac+2ad−3bc−3bd2ac+2ad-3bc-3bd  

a)

 (c−d)(2a−3b)\left(c-d\right)\left(2a-3b\right)  

b)

 (c+d)(2a−3b)\left(c+d\right)\left(2a-3b\right)  

c)

 (c+d)(2a+3b)\left(c+d\right)\left(2a+3b\right)  

d)

 (c+d)(a−b)\left(c+d\right)\left(a-b\right)  

8.

 m(n−2)+2−nm(n-2)+2-n  

a)

 (m−2)(n−1)\left(m-2\right)\left(n-1\right)  

b)

 (n−2)(m−1)\left(n-2\right)\left(m-1\right)  

c)

 (n−2)(m+1)\left(n-2\right)\left(m+1\right)  

d)

 (m+2)(n−1)\left(m+2\right)\left(n-1\right)  

9.

 −12tz2+14tz3−18tz4-\frac{1}{2}tz^2+\frac{1}{4}tz^3-\frac{1}{8}tz^4  

a)

 12tz2(−4+2z−z2)\frac{1}{2}tz^2\left(-4+2z-z^2\right)  

b)

 18t2z2(−4+2z−z2)\frac{1}{8}t^2z^2\left(-4+2z-z^2\right)  

c)

 12t2z2(−4+2z−z2)\frac{1}{2}t^2z^2\left(-4+2z-z^2\right)  

d)

 18tz2(−4+2z−z2)\frac{1}{8}tz^2\left(-4+2z-z^2\right)  

10.

 c(x−3y)+d(3y−x)c(x-3y)+d(3y-x)  

a)

 (x−3y)(c−d)\left(x-3y\right)\left(c-d\right)  

b)

 (3x−y)(c−d)\left(3x-y\right)\left(c-d\right)  

c)

 (3y−x)(c−d)\left(3y-x\right)\left(c-d\right)  

d)

 (x−3y)(c+d)\left(x-3y\right)\left(c+d\right)  

11.

 3ax+2by−2bx−6a−3ay+4b3ax+2by-2bx-6a-3ay+4b  

a)

 (x−y+2)(3a−2b)\left(x-y+2\right)\left(3a-2b\right)  

b)

 (x−y−2)(3a+2b)\left(x-y-2\right)\left(3a+2b\right)  

c)

 (x−y−2)(3a−2b)\left(x-y-2\right)\left(3a-2b\right)  

d)

 (x+y−2)(3a+2b)\left(x+y-2\right)\left(3a+2b\right)  

12.

 (a+3)(a+1)−4(a+1)(a+3)(a+1)-4(a+1)  

a)

 (a+1)(a−2)\left(a+1\right)\left(a-2\right)  

b)

 (a+1)(a+1)\left(a+1\right)\left(a+1\right)  

c)

 (a−1)(a−1)\left(a-1\right)\left(a-1\right)  

d)

 (a+1)(a−1)\left(a+1\right)\left(a-1\right)  

13.

 64(x+y)2−121(x−2)264(x+y)^2-121(x-2)^2  

a)

 (19x+8y−22)(−3x+8y+22)\left(19x+8y-22\right)\left(-3x+8y+22\right)  

b)

 (−3x+8y+22)(−3x+8y−22)\left(-3x+8y+22\right)\left(-3x+8y-22\right)  

c)

 (3x+8y+22)(3x+8y−22)\left(3x+8y+22\right)\left(3x+8y-22\right)  

d)

 (−3x+8y−22)(−3x+8y+22)\left(-3x+8y-22\right)\left(-3x+8y+22\right)  

14.

 −6t2w+12tw2−3t2w+6tw-6t^2w+12tw^2-3t^2w+6tw  

a)

 3tw(2t+4w−t+2)3tw\left(2t+4w-t+2\right)  

b)

 3tw(−2t+4w−t)3tw\left(-2t+4w-t\right)  

c)

 3tw(−2t+4w−t+2)3tw\left(-2t+4w-t+2\right)  

d)

 3tw(−2t+4w−2t+2)3tw\left(-2t+4w-2t+2\right)  

15.

 100169m2n6−225t4y4a4b6\frac{100}{169}m^2n^6-\frac{225t^4y^4}{a^4b^6}  

a)

 (1013mn2+15t2y2a2b3)(1013mn2−15t2y2a2b3)\left(\frac{10}{13}mn^2+\frac{15t^2y^2}{a^2b^3}\right)\left(\frac{10}{13}mn^2-\frac{15t^2y^2}{a^2b^3}\right)  

b)

 (1013m2n3+15t2y2a2b3)(1013m2n3−15t2y2a2b3)\left(\frac{10}{13}m^2n^3+\frac{15t^2y^2}{a^2b^3}\right)\left(\frac{10}{13}m^2n^3-\frac{15t^2y^2}{a^2b^3}\right)  

c)

 (1013mn3+15t2y2a2b3)(1013mn3−15t2y2a2b3)\left(\frac{10}{13}mn^3+\frac{15t^2y^2}{a^2b^3}\right)\left(\frac{10}{13}mn^3-\frac{15t^2y^2}{a^2b^3}\right)  

d)

 (1013mn3+15t2y2ab3)(1013mn3−15t2y2ab3)\left(\frac{10}{13}mn^3+\frac{15t^2y^2}{ab^3}\right)\left(\frac{10}{13}mn^3-\frac{15t^2y^2}{ab^3}\right)  

16.

 (1+3n)(m+1)−2n(m+1)+3(m+1)(1+3n)(m+1)-2n(m+1)+3(m+1)  

a)

 (m+1)(2n+4)\left(m+1\right)\left(2n+4\right)  

b)

 (m+1)(n−4)\left(m+1\right)\left(n-4\right)  

c)

 (m+1)(n+4)\left(m+1\right)\left(n+4\right)  

d)

 (m+1)(n+3)\left(m+1\right)\left(n+3\right)  

17.

 a3+a2+a+1+x2+ax2a^3+a^2+a+1+x^2+ax^2  

a)

 (a+1)(a2−x2−1)\left(a+1\right)\left(a^2-x^2-1\right)  

b)

 (a+1)(a2+x2−1)\left(a+1\right)\left(a^2+x^2-1\right)  

c)

 (a−1)(a2+x2+1)\left(a-1\right)\left(a^2+x^2+1\right)  

d)

 (a+1)(a2+x2+1)\left(a+1\right)\left(a^2+x^2+1\right)  

18.

 25m2n−(3x+2y)425m^{2n}-(3x+2y)^4  

a)

 (5m+(3x+2y)2)(5m−(3x+2y)2)\left(5m^{ }+\left(3x+2y\right)^2\right)\left(5m^{ }-\left(3x+2y\right)^2\right)  

b)

 (5mn+(3x+2y))(5mn−(3x+2y))\left(5m^n+\left(3x+2y\right)^{ }\right)\left(5m^n-\left(3x+2y\right)^{ }\right)  

c)

 (5mn+(3x+2y)2)(5mn−(3x+2y)2)\left(5m^n+\left(3x+2y\right)^2\right)\left(5m^n-\left(3x+2y\right)^2\right)  

d)

 (5m2n+(3x+2y)2)(5m2n−(3x+2y)2)\left(5m^{2n}+\left(3x+2y\right)^2\right)\left(5m^{2n}-\left(3x+2y\right)^2\right)  

19.

 25x2yz+30xy2z−60x3yz225x^2yz+30xy^2z-60x^3yz^2  

a)

 5xyz2(5x+6y−12x2z)5xyz^2\left(5x+6y-12x^2z\right)  

b)

 5xyz(5x+6y−12x2z)5xyz\left(5x+6y-12x^2z\right)  

c)

 5xz(5x+6y−12x2z)5xz\left(5x+6y-12x^2z\right)  

d)

 5xyz(5x+6y−12xz)5xyz\left(5x+6y-12xz\right)  

20.

  (3x−4y)8225 −t4\ \frac{(3x-4y)^8}{225}\ -t^4  

a)

 ((3x−y)215+t2)((3x−y)215−t2)\left(\frac{\left(3x-y\right)^2}{15}+t^2\right)\left(\frac{\left(3x-y\right)^2}{15}-t^2\right)  

b)

 ((3x−y)415+t2)((3x−y)415−t2)\left(\frac{\left(3x-y\right)^4}{15}+t^2\right)\left(\frac{\left(3x-y\right)^4}{15}-t^2\right)  

c)

 ((3x−y)15+t2)((3x−y)15−t2)\left(\frac{\left(3x-y\right)^{ }}{15}+t^2\right)\left(\frac{\left(3x-y\right)^{ }}{15}-t^2\right)  

d)

 ((3x−y)215+t)((3x−y)215−t)\left(\frac{\left(3x-y\right)^2}{15}+t^{ }\right)\left(\frac{\left(3x-y\right)^2}{15}-t^{ }\right)