Question

procedimiento : )
de cada una : )

Answer 1

Explicación paso a paso:

1) $7r+14s=7(\frac{7}{7}r+\frac{14}{7}s)=7(r+2s)$

2) $5a^2+3a=a(5\frac{a^2}{a}+3\frac{a}{a})=a(5a+3)$

3) $10ab-12a^2b=2ab(\frac{10ab}{2ab} -\frac{12aba}{2ab})=2ab(5-12a)$

4) $27u^4v^5-63u^3v^6=9u^3v^4(\frac{27u^3v^4u}{9u^3v^4} -\frac{63u^3v^4v}{9u^3v^4})=9u^3v^4(3u-7v)$

5) $12z-30z^2+6z^3=6z(\frac{12z}{6z}-\frac{30zz}{6z}+\frac{6zz^2}{6z})=6z(2-5z+z^2)$

6) $14a^5b^2+28a^2b^4-21a^2b^3=\\ 7a^2b^2(\frac{14a^2b^2a^3}{7a^2b^2}+ \frac{28a^2b^2b^2}{7a^2b^2}- \frac{21a^2b^2b}{7a^2b^2} )\\ =7a^2b^2(2a^3+4b^2-3b)$

7) $40a^4b^6-48a^3b^5-16a^5b^3=8a^3b^3(\frac{40a^3b^3ab^3}{8a^3b^3}- \frac{48a^3b^3b^2}{8a^3b^3}- \frac{16a^3b^3a^2}{8a^3b^3} )\\=8a^3b^3(5ab^3-6b^2-2a^2)$

8) $4a^2b^4-2a^3b^2-6a^2=2a^2(\frac{4a^2b^4}{2a^2}- \frac{2a^2ab^2}{2a^2}- \frac{6a^2}{2a^2} )=2a^2(2b^4-ab^4-3)$

9) $12m^5n^2+9m^4n+6m^3n^2=3m^3n(\frac{12m^3nm^2n}{3m^3n} +\frac{9m^3nm}{3m^3n} +\frac{6m^3nn}{3m^3n} )\\ =3m^3n(4m^2n+3m+2n)$

10) tiene dos resultados

primer resultado:

$-5x^6y^2+15x^4y^4-10x^2y^6=5x^2y^2(-\frac{5x^2y^2x^4}{5x^2y^2} +\frac{15x^2y^2x^2y^2}{5x^2y^2} -\frac{10x^2y^2y^4}{5x^2y^2} )\\=5x^2y^2(-x^4+3x^2y^2-2y^4)$

Segundo resultado:

$-5x^6y^2+15x^4y^4-10x^2y^6=-5x^2y^2(\frac{5x^2y^2x^4}{5x^2y^2} -\frac{15x^2y^2x^2y^2}{5x^2y^2} +\frac{10x^2y^2y^4}{5x^2y^2} )\\=-5x^2y^2(x^4-3x^2y^2+2y^4)$