Question

Factorize x( x - 2)( x - 4) + 4x - 8

Answer 1

= x ( x - 2)( x - 4) + 4 ( x - 2)

Taking ( x - 2) common in both terms

= ( x - 2){x ( x - 4) + 4}

= ( x - 2){x2 - 4x + 4}

Now splitting middle term of x² - 4x + 4

= ( x - 2){x²  - 2x - 2x + 4}

= ( x - 2){x ( x - 2) - 2 ( x - 2)}

= ( x - 2){( x - 2)( x - 2)}

= ( x - 2)( x - 2)( x - 2)

= ( x - 2)³

∴ x ( x - 2)( x - 4) + 4x - 8 = ( x - 2)³