Question

Factorise : 4a^7 - 256ab^6

Answer 1

$Given \: 4a^{7} - 256ab^{6}$

$= 4a( a^{6} - 64b^{6} )$

$= 4a[ (a^{3})^{2} - (8b^{3})^{2}$

/* By algebraic identity */

$=4a( a^{3} + 8b^{3})( a^{3} - 8b^{3} )$

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

$= 4a(a+2b)[a^{2}-a\times 2b+(2b)^{2}](a-2b)[a^{2}+a\times 2b+(2b)^{2}]$

$= 4a(a+2b)(a^{2}-2ab+4b^{2}](a-2b)(a^{2}+2ab+4b^{2})$

Therefore.,

$\red{ 4a^{7} - 256ab^{6}}$

$\green {= 4a(a+2b)(a^{2}-2ab+4b^{2}](a-2b)(a^{2}+2ab+4b^{2})}$

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