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Factorize Each of the Following Algebraic Expression: 4x4 + Y4 - Mathematics

Sum

Factorize each of the following algebraic expression:
4x4 + y4

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Solution

\[4 x^4 + y^4 \]
\[ = 4 x^4 + 4 x^2 y^2 + y^4 - 4 x^2 y^2 \]
\[ = [(2 x^2 )^2 + 2 \times 2 x^2 \times y + ( y^2 )^2 ] - (2xy )^2 \]
\[ = (2 x^2 + y^2 )^2 - (2xy )^2 \]
\[ = [(2 x^2 + y^2 ) - 2xy][(2 x^2 + y^2 ) + 2xy]\]
\[ = (2 x^2 - 2xy + y^2 )(2 x^2 + 2xy + y^2 )\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 7 Factorization
Exercise 7.6 | Q 15 | Page 23
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