Question

ayuden por favor nesecito las respuestas de estos trinomios simples y compuestos:
a) (a-1)²+3(a-1)-108=
b) 15a²-8a-12=
c) 30m²+17am-21a²=
d) 6m²-13am-15a²=
e) 7x⁶-33x³-10=

Answer 1

$a)\left(a-1\right)^2+3\left(a-1\right)-108$
$Para\: (a-1)^{2}\:aplicar\:la\:siguiente\:regla\:de\:productos\:notables:$
(a-b)²=a²-2ab+b²
$=a^2-2a+1+3(a-1)-108$
$\mathrm{Poner\:los\:parentesis\:utilizando}:\quad \:a\left(b+c\right)=ab+ac$
$=a^2-2a+1+3a-3-108$
$=a^2+a-110$

$b)15a^2-8a-12$
$=\left(15a^2+10a\right)+\left(-18a-12\right)$
$\mathrm{Factorizar\:}5a\mathrm{\:de\:}15a^2+10a\mathrm{:\quad }5a\left(3a+2\right)$
$\mathrm{Factorizar\:}-6\mathrm{\:de\:}-18a-12\mathrm{:\quad }-6\left(3a+2\right)$
$=5a\left(3a+2\right)-6\left(3a+2\right)$
$=\left(3a+2\right)\left(5a-6\right)$

$c)30m^2+17am-21a^2$
$=\left(30m^2-18ma\right)+\left(35ma-21a^2\right)$
$\mathrm{Factorizar\:}6m\mathrm{\:de\:}30m^2-18ma\mathrm{:\quad }6m\left(5m-3a\right)$
$\mathrm{Factorizar\:}7a\mathrm{\:de\:}35ma-21a^2\mathrm{:\quad }7a\left(5m-3a\right)$
$=6m\left(5m-3a\right)+7a\left(5m-3a\right)$
$\mathrm{Factorizar\:el\:termino\:comun\:}\left(5m-3a\right)$
$=\left(5m-3a\right)\left(6m+7a\right)$

$d)\:6m^2-13am-15a^2$
$=\left(6m^2+5ma\right)+\left(-18ma-15a^2\right)$
$=m\left(6m+5a\right)-3a\left(6m+5a\right)$
$=\left(6m+5a\right)\left(m-3a\right)$