Question

розкласти на множники 4m²-12mn+9²​

Answer 1

Ответ:

$a)\ \ 4m^2-12mn+9n^2=\underbrace{(2m)^2-2\cdot (2m)\cdot 3n+(3n)^2}_{a^2-2ab+b^2=(a-b)^2}=(2m-3n)^2\\\\\\\\b)\ \ 4m^2-12mn+9^2=(2m-3n)^2-9n^2+81=(2m-3n)^2-(9n^2-81)=\\\\=\Big(2m-3n-\sqrt{9n^2-81}\Big)\Big(2m-3n+\sqrt{9n^2-81}\Big)=\\\\=\Big(2m-3n-3\sqrt{n^2-9}\Big)\Big(2m-3n+3\sqrt{n^2-9}\Big)\\\\n\in (-\infty ;-3\, ]\cup [\ 3\, ;+\infty \, )$