Instrucciones: Responde las siguientes preguntas

• Factoriza la siguiente expresión algebraica. $$216x^{18}y^{42}-2 \ 197z^{30}$$
  • $$\left ( 6x^{6}y^{14}-13z^{10} \right )\left ( 36x^{12}y^{28}+78x^{6}y^{14}z^{10}+169z^{20} \right )$$
  • $$\left ( 6x^{9}y^{21}-13z^{15} \right )\left ( 36x^{18}y^{42}+78x^{9}y^{21}z^{15}+169z^{30} \right )$$
  • $$\left ( 6x^{9}y^{21}-17z^{15} \right )\left ( 36x^{18}y^{42}+102x^{9}y^{21}z^{15}+289z^{30} \right )$$
  • $$\left ( 6x^{6}y^{14}-17z^{10} \right )\left ( 36x^{12}y^{28}+102x^{6}y^{14}z^{10}+289z^{20} \right )$$

• Factoriza la siguiente expresión algebraica. $$8a^{6}-343b^{12}$$
  • $$\left ( 2a^{3}-7b^{6} \right )\left ( 4a^{6}+14a^{3}b^{6}+49b^{12} \right )$$
  • $$\left ( 2a^{2}-7b^{4} \right )\left ( 4a^{4}+14a^{2}b^{4}+49b^{8} \right )$$
  • $$\left ( 2a^{2}-7b^{4} \right )\left ( 4a^{4}-14a^{2}b^{4}-49b^{8} \right )$$
  • $$\left ( 2a^{3}-7b^{6} \right )\left ( 4a^{6}-14a^{3}b^{6}-49b^{12} \right )$$

• Factoriza la siguiente expresión algebraica. $$512a^{3}-27$$
  • $$\left ( 8a-3 \right )\left ( 64a^{2}-11a-9 \right )$$
  • $$\left ( 8a-3 \right )\left ( 64a^{2}-24a-9 \right )$$
  • $$\left ( 8a-3 \right )\left ( 64a^{2}+24a+9 \right )$$
  • $$\left ( 8a-3 \right )\left ( 64a^{2}+11a+9 \right )$$

• Factoriza la siguiente expresión algebraica. $$42 \ 875a^{33}b^{48}-85 \ 184c^{24}d^{30}$$
  • $$\left ( 45a^{11}b^{16}-34c^{12}d^{15} \right )\left ( 2 \ 025a^{22}b^{32}+1 \ 530a^{11}b^{16}c^{12}d^{15}+1 \ 156c^{24}d^{30} \right )$$
  • $$\left ( 35a^{11}b^{16}-44c^{12}d^{15} \right )\left ( 1 \ 225a^{22}b^{32}+1 \ 540a^{11}b^{16}c^{12}d^{15}+1 \ 936c^{24}d^{30} \right )$$
  • $$\left ( 45a^{11}b^{16}-34c^{8}d^{10} \right )\left ( 2 \ 025a^{22}b^{32}+1 \ 530a^{11}b^{16}c^{8}d^{10}+1 \ 156c^{16}d^{20} \right )$$
  • $$\left ( 35a^{11}b^{16}-44c^{8}d^{10} \right )\left ( 1 \ 225a^{22}b^{32}+1 \ 540a^{11}b^{16}c^{8}d^{10}+1 \ 936c^{16}d^{20} \right )$$

• Factoriza la siguiente expresión algebraica. $$64m^{12}n^{33}-1 \ 331p^{27}$$
  • $$\left ( 4m^{4}n^{11}-11p^{3} \right )\left ( 16m^{16}n^{121}+44m^{4}n^{11}p^{3}+121p^{9} \right )$$
  • $$\left ( 4m^{4}n^{11}-11p^{9} \right )\left ( 16m^{8}n^{22}+44m^{4}n^{11}p^{9}+121p^{18} \right )$$
  • $$\left ( 4m^{4}n^{11}-11p^{9} \right )\left ( 16m^{16}n^{121}+44m^{4}n^{11}p^{9}+121p^{81} \right )$$
  • $$\left ( 4m^{4}n^{11}-11p^{3} \right )\left ( 16m^{8}n^{22}+44m^{4}n^{11}p^{3}+121p^{6} \right )$$