Factorize 4( X - Y)2 -12( X - Y)( X + Y ) + 9(X + Y )2 - Mathematics

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Factorize 4( x - y)2  -12( x - y)( x + y ) + 9(x + y )2

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Solution

Let ( x - y ) = a, ( x + y ) = b

= 4a2 -12ab + 9b2

Splitting middle term -12 = -6 - 6 also 4 x 9 = -6 x -6

= 4a2 - 6ab - 6ab + 9b2

= 2a (2a - 3b) - 3b (2a - 3b)

= (2a - 3b)(2a - 3b)

= (2a - 3b)2

Substituting a = x - y and b = x + y

=[2 ( x - y ) - 3( x + y )]

= [2x - 2 y - 3x - 3y]2

= [2x - 3x - 2 y - 3y]2

= [-x - 5 y]2

 = [(-1)(x + 5y)]           [∵ (-1)2 = 1]

∴ 4( x - y)2 -12( x - y)( x + y) + 9( x + y )2  = (x + 5y)2

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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 22 | Page 9

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