Question

Factorize :-
(x^2 - 2x)^2 - 2(x^2 - 2x) - 3

Answer 1

Answer:

$\tt \:  Factorize : \: ( { {x}^{2} - 2x) }^{2} - 2 {( {x}^{2} - 2x) } - 3$

Step-by-step explanation:

$\tt \:  \longrightarrow \: ( { {x}^{2} - 2x) }^{2} - 2 {( {x}^{2} - 2x) } - 3$

$\tt \:  \longrightarrow \: \boxed{ \red{\tt \: Let \: {x}^{2} - 2x = y }}$

☆ So, given expression can be rewritten as

$\tt \:  \longrightarrow \: {y}^{2} - 2y - 3$

$\tt \:  \longrightarrow \: {y}^{?} - 3y + y - 3$

$\tt \:  \longrightarrow \: y(y - 3) + 1(y - 3)$

$\tt \:  \longrightarrow \: (y - 3)(y + 1)$

☆ On substituting the value of y, we get

$\tt \:  \longrightarrow \: ( {x}^{2} - 2x - 3)( {x}^{2} - 2x + 1)$

$\tt \:  \longrightarrow \: ( {x}^{2} - 3x + x - 3)( {x}^{2} - 2 \times x \times 1 + {(1)}^{2} )$

$\tt \:  \longrightarrow \: \bigg(x(x - 3) + 1(x - 3) \bigg) ( {(x - 1)}^{2}$

$\tt \:  \longrightarrow \: (x - 3)(x + 1)(x - 1)(x - 1)$