Factorize: $( y+\frac{1}{y})^{2}-5( y+\frac{1}{y})+4$.

Given: $( y+\frac{1}{y})^{2}-5( y+\frac{1}{y})+4$.

To do: To factorize: $( y+\frac{1}{y})^{2}-5( y+\frac{1}{y})+4$.

Solution:

Let $( y+\frac{1}{y})=x$,

$=( y+\frac{1}{y})^{2}-5( y+\frac{1}{y})+4$

$=x^2-5x+4$

$=x^2-4x-x+4$

$=x( x-4)-1( x-4)=0$

$=( x-4)( x-1)$

$=( y+\frac{1}{y}-4)( y+\frac{1}{y}-1)$

Tutorialspoint

Updated on: 10-Oct-2022

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