Factorize X2 - Y2 - 4xz + 4z2 - Mathematics

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Factorize x2 - y2 - 4xz + 4z2

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Solution

On rearranging the terms

= x2  - 4xz + 4z2 - y2

= (x)2  - 2 x  x  2z + (2z )2  - y2

Using identity a2  - 2ab + b2  = (a - b)2

= ( x - 2z )2  - y2

Using identity a2 - b2 = (a + b)(a - b)

= ( x - 2z + y )( x - 2z - y )

∴ x2  - y2  - 4xz + 4z2  = ( x - 2z + y )( x - 2z - y)

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

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.1 | Q 12 | Page 9

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