50) Factorize: 81a4 – 16b4
Answers
81 a^4 - 16 b^4
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= (9 a^2 )^2 - ( 4 b^2 )^2
= ( 9 a^2 - 4 b^2 ) ( 9 a^2 + 4 b^2 )
= {(3 a)^2 - (2 b )^2} { ( 3a )^2 +( 2b )^2 }
= (3 a - 2 b ) ( 3 a + 2 b ) {( 3a + 2b )^2 - 2(3a)(2b) }
= (3a - 2b ) ( 3a + 2b ) { 3a + 2b)(3a+2b) - 12 ab }
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Answer:
Step-by-step explanation: We have 81a2 - 16b4 = (9a2)2 - (4b2)2
= left parenthesis 9 straight a squared space plus space 4 straight b squared right parenthesis space left parenthesis 9 straight a squared space minus space 4 straight b squared right parenthesis
[Using A2 - B2 = (A + B)(A - B)]
= left parenthesis 9 straight a squared space plus space 4 straight b squared right parenthesis space left square bracket left parenthesis 3 straight a right parenthesis squared space minus space left parenthesis 2 straight a right parenthesis squared right square bracket
=space space space space left parenthesis 9 straight a squared space plus space 4 straight b squared right parenthesis space left square bracket left parenthesis 3 straight a space plus space 2 straight b right parenthesis left parenthesis 3 straight a space minus 2 straight b right parenthesis right square bracket
= left parenthesis 9 straight a squared space plus space 4 straight b squared right parenthesis left parenthesis 3 straight a space plus space 2 straight b right parenthesis left parenthesis 3 straight a space minus space 2 straight b right parenthesis