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

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

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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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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.1 [Page 9]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.1 | Q 8 | Page 9

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