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CBSE Class 8 Answered

Hi,Sir I wanna know that why we add or subtract something when we factorize algebraic expressions like 4 x to the power of 4 space end exponent plus space y to the power of 4 to the power of blank end exponent 
Asked by SPARSH | 26 Feb, 2016, 01:47: PM
answered-by-expert Expert Answer

This expression does not appear to factor, since there is no identity for the sum of squares.

However, by adding and subtracting the term, we arrive at a difference of squares.

begin mathsize 14px style 4 x to the power of 4 plus y to the power of 4 equals 4 x to the power of 4 plus 4 x squared y squared plus y to the power of 4 minus 4 x squared y squared space space space... open parentheses Adding space and space subtracting space 4 straight x squared straight y squared space close parentheses equals left parenthesis 2 x squared plus y squared right parenthesis squared minus left parenthesis 2 x y right parenthesis squared space space space space space space space space space space.... left square bracket sin c e space left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared equals left parenthesis 2 x squared plus y squared minus 2 x y right parenthesis left parenthesis 2 x squared plus y squared plus 2 x y right parenthesis space space space space space space space.... left square bracket S i n c e space a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis right square bracket end style

Answered by | 26 Feb, 2016, 06:03: PM

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