Question

решите уравнение z(8-z)-(z-8)=0
разложите на множители 49 – 4y2+4xy – x2

Answer 1

z(8-z)+(8-z)=0
(8-z)(z+1)=0
8-z=0⇒z=8
z+1=0⇒z=-1
49 – 4y²+4xy – x²=7²-(2y-x)²=(7+2y-x)(7-2y+x)

Answer 2

$1) z(8-z)-(z-8)=0 \ -z(z-8)-(z-8)=0 \ (z-8)(-z-1)=0rightarrow -(z-8)(z+1)=0rightarrow (z-8)(z+1)=0 \ \ z+1=0rightarrow z_1=-1 \ z-8=0rightarrow z_2=8$
$49-4y^2+4xy-x^2=-(x^2-4xy+4y^2)+49= \ =-(x-2y)^2+7^2=7^2-(x-2y)^2= \ =(7-(x-2y))(7+(x-2y))=(7-x+2y)((7+x-2y)$