Question

Pls resolve this into factors.
$( {x}^{2} - 2x) {}^{2} + 5( {x }^{2} - 2x) - 36$
Pls anwer with explanation.​

Answer 1

Question -

$\sf{\color{teal} { Factorise \: the \: given \: expression\: - }}$

$( {x}^{2} - 2x) {}^{2} + 5( {x }^{2} - 2x) - 36$

Solution -

• $\sf{\color{teal} { Method \: 1 }}$

$( {x}^{2} - 2x) {}^{2} + 5( {x }^{2} - 2x) - 36 \\ \\ => ({x}^{2} - 2x) {}^{2} +9( {x }^{2} - 2x) - 4 ( {x}^2 -2x) - 36 \\ \\ => ( {x}^{2} - 2x)( {x}^{2} - 2x + 9) \: - 4( {x}^{2} - 2x + 9) \\ \\ = > ( {x}^{2} - 2x + 9)( {x}^{2} - 2x - 4)$

• $\sf{ \color{teal}{ Method \: 2 }}$

$( {x}^{2} - 2x) {}^{2} + 5( {x }^{2} - 2x) - 36 \\ \\ \sf{ Let \:( {x}^{2} - 2x) = k } \\ \\ => {k}^2 + 5k - 36 \\ \\ => {k}^2 + 9k - 4k - 36 \\ \\ => k( k+9) -4(k+9) \\ \\ => (k+9)(k-4) \\ \\ \sf{ Substuting \: the \: value \: of \: k } \\ \\ => ( {x}^{2} - 2x + 9)( {x}^{2} - 2x - 4)$