Question
Factorise :$5a^2- b^2- 4ab+ 7a - 7b$
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Answer
$5a^2- b^2- 4ab+ 7a - 7b$
$= 4a^2 + a^2 - b^2 - 4ab + 7a - 7b$
$= a^2 - b^2 + 4a^2 - 4ab + 7a - 7b$
$= ( a^2 - b^2 ) + 4a( a - b ) + 7( a - b )$
$= ( a - b )( a + b ) + 4a( a - b ) + 7( a - b ) [ \because a^2 - b^2 = ( a + b )( a - b ) ]$
$= ( a - b )[ ( a + b ) + 4a + 7 ]$
$= ( a - b )[ ( a + b ) + 4a + 7 ]$
$= ( a - b )[ 5a + b + 7 ]$
$= 4a^2 + a^2 - b^2 - 4ab + 7a - 7b$
$= a^2 - b^2 + 4a^2 - 4ab + 7a - 7b$
$= ( a^2 - b^2 ) + 4a( a - b ) + 7( a - b )$
$= ( a - b )( a + b ) + 4a( a - b ) + 7( a - b ) [ \because a^2 - b^2 = ( a + b )( a - b ) ]$
$= ( a - b )[ ( a + b ) + 4a + 7 ]$
$= ( a - b )[ ( a + b ) + 4a + 7 ]$
$= ( a - b )[ 5a + b + 7 ]$
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