Factorise :8a^3- b^3- 4ax + 2bx - Vidyadip

Question

Factorise $:8a^3- b^3- 4ax + 2bx$

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Answer

We know that,
$a^3 - b^3 = ( a - b )( a^2 + ab + b^2 ) .....(1)$
$8a^3- b^3- 4ax + 2bx$
$= [ (2a)^3 - (b)^3 ] - 2 \times ( 2a - b )$
$= ( 2a - b )[ (2a)^2 + 2a \times b + (b)^2 ] - 2 x ( 2a - b ) [$ From$(1) ]$
$= ( 2a - b )[ 4a^2 + 2ab + b^2 ] - 2 \times ( 2a - b )$
$= ( 2a - b )[ 4a^2 + 2ab + b^2 - 2x ]$

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