Question

factorise: 3a^7-192a
please answer I will mark it as brainlist Answer​

Answer 1

$Given \: Algebraic \: Expression : 3a^{7}- 192a$

$= 3a \times a^{6} - 3\times 64 \: a$

$= 3a( a^{6} - 64 )$

$= 3a[ (a^3)^{2} - 8^{2} ]$

$= 3a(a^{3} + 8 ) ( a^{3} - 8 )$

/* By Algebraic Identity */

$\boxed{\pink { x^{2} - y^{2} = ( x + y )( x - y ) }}$

$= 3a (a^{3} + 2^{3})(a^{3} - 2^{3} )$

$= 3a(a+2)(a^{2} - a \times 2 + 2^{2} )(a-2)(a^{2} +a \times 2 + 2^{2} )$

/* By Algebraic Identities */

$\blue { 1. x^{3} + y^{3} = (x+y)(x^{2} - xy + y^{2} )}$

$\blue { 2. x^{3} - y^{3} = (x-y)(x^{2} + xy + y^{2} )}$

$= 3a(a+2)(a^{2} - 2a + 4 )(a-2)(a^{2} +2a + 4 )$

Therefore.,

$\red{ Factors \: of \: 3a^{7} - 192a }$

$\green {= 3a(a+2)(a^{2} - 2a + 4 )(a-2)(a^{2} +2a + 4 )}$

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