Question

factorice ( x² - 4x ) ( x² - 4x - 1 ) - 20 fast plz ​

Answer 1

$:\mapsto\bf{(x^2-4x)(x^2-4x-1)-20}$

$:\mapsto\sf{(x^2 - 4x)[(x^2 - 4x) - 1] - 20}$

$:\mapsto\sf{(x^2 - 4x)^2 - (x^2 - 4x) - 20}$

$\leasto\bf{ y^2 - y - 20 , where \:y = x^2 - 4x}$

$:\mapsto\sf{ y^2 + 4y - 5y - 20}$

$:\mapsto\sf{ y(y+4) - 5(y+4)}$

$:\mapsto\sf{ (y+4)(y-5)}$

$:\mapsto\sf{ (x^2 - 4x + 4)(x^2 - 4x - 5)}\bf{ [Replacing\: y \:by\: x^2-4x]}$

$:\mapsto\sf{\{x(x-2) - 2(x-2)} {x(x+1) - 5(x+1)\}}$$:\mapsto\sf{\{x^2 - 2x - 2x + 4}{x^2 + x - 5x - 5\}}$

$:\mapsto\sf{\{(x-2)(x-2)} {(x+1)(x-5)\}}$

$:\mapsto{\boxed{\bf{\red{ (x+1)(x-2)(x-2)(x-5)}}}$