Question

Как разложить на множетели:
3x^2-12
32a^4b-2a^2b
2m^2+2n^2-4mn
12m^5n+24m^4n+12m^3n
(x^2+2x)^2-1
81-(y^2+6y)^2

Answer 1

$3 x^2-12=3(x^2-4)=3(x-2)(x+2)$
$32a^4b-2a^2b=2a^2b(16a^2-1)=2a^2b(4a-1)(4a+1)$
$2m^2+2n^2-4mn=( msqrt{2} -n sqrt{2} )^2$
$12m^5n+24m^4n+12m^3n = 12m^3n(m^2+2m+1)=12m^3n(m+1)^2$
$(x^2+2x)^2-1=(x^2+2x-1)(x^2+2x+1)=(x^2+2x-1)(x+1)^2$
$81-(y^2+6y)^2=(9 - (y^2+6y))(9+y^2+6y) = (9-y^2-6y)(y+3)^2$