Question

Разложите на множители
а)mn^2-9mn^4=
б)x^4-4x^3+16x-16=

Answer 1

$а)mn^2-9mn^4 = \\ = m{n}^{2} (1 - 9 {n}^{2} ) = \\ = m {n}^{2} (1 - 3n)(1 + 3n)$
$б)x^4-4x^3+16x-16 = \\ = (x^4-16) - (4 {x}^{3} - 16x)= \\ = ( {x}^{2} - 4)( {x}^{2} + 4) - 4x( {x}^{2} - 4) = \\ = ( {x}^{2} - 4)( {x}^{2} + 4 - 4x) = \\ = (x - 2)(x + 2)(x - 2)^{2} = \\ = (x + 2) ({x - 2})^{3}$