Question

Actividad 4: Factorizar los siguientes polinomios a través de la diferencia de cuadrados.
a. 4c2 − 1 =
b. 25a4b4 − 16c2 =
c.1/36x2 − x8 =
d. x2/100 − y2z4/81 =
e. −169y6 + 100m2n10 =
f. −49b12 + a18 =

Answer 1

Respuesta:

a.- $4c^{2}-1 = (4c+1)(4c-1)$

$\sqrt{4c^{2}} = 4c$

$\sqrt{1} = 1$

b.- $25a^{4} b^{4}-16c^{2}= (5a^{2} b^{2}+4c)(5a^{2} b^{2}-4c)$

$\sqrt{25a^{4} b^{4} } =5a^{2} b^{2}$

$\sqrt{16c^{2} } =4c$

e.- $-169y^{6}+100m^{2} n^{10} = (13y^{3}+10m^{} n^{5})(13y^{3} -10m^{} n^{5} )$

$\sqrt{169y^{6} } = 13y^{3}$

$\sqrt{100m^{2}n^{10} } =10m^{} n^{5}$

f.- $-49b^{12} +a^{18} =(7b^{6}+ a^{9} )(7b^{6}- a^{9} )$

$\sqrt{49b^{12} } =7b^{6}$

$\sqrt{a^{18} }=a^{9}$

c.- $\frac{1}{36}x^{2} -x^{8}=(\frac{1}{6}x+x^{4})(\frac{1}{6}x-x^{4} )$

$\sqrt{\frac{1}{36^{} } }x^{2} =\frac{1}{6} x$

$\sqrt{x^{8} } =x^{4}$

d.- $\frac{x^{2} }{100} -\frac{y^{2}z^{4} }{81 } =(\frac{x}{10} +\frac{y z^{2} }{9}) (\frac{x}{10} -\frac{y z^{2} }{9})$

$\sqrt{\frac{x^{2} }{100} } =\frac{x^{} }{10}$

$\sqrt{\frac{y^{2} z^{4} }{81} } =\frac{yz^{2} }{ 9}$