Factorize X4 + X2 Y2 + Y4 - Mathematics

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Factorize x4 + x2 y2 + y4

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Solution

Adding x2 y2 and subtracting x2 y2 to the given equation.

= x4 + x2 y2 + y4 + x2 y2 - x2 y2

= x4 + 2x2 y2 + y4 - x2 y2

= (x2 )2  + 2 x x2 x y2  + ( y2 )2  - ( xy)2

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

= (x2  + y2 )2  - ( xy)2

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

= (x2  + y2  + xy)(x2  + y2  - xy )

∴ x4  + x2 y2  + y4   = (x2  + y2  + xy)(x2  + y2  - xy)

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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 25 | Page 9

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