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Question
Factorize x( x - 2)( x - 4) + 4x - 8
Solution
= 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
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