Question

$1 - (2x + 3y) - 6(2x + 3y) {}^{2}$
factorise

Answer 1

Hey friend ☺

1 - ( 2x + 3y ) - 6 ( 2x + 3y )^2

Let ( 2x + 3y ) = a

1 - a + 6a^2

= 6a^2 - a + 1

Product should be 6 and sum should be - 1

such pair is - 3 & 2

= 6a^2 - 3a + 2a - 1

= 3a ( 2a - 1 ) + 1 ( 2a - 1 )

= ( 3a + 1 )( 2a - 1 )

putting value of a back in the equation

= [ 3 ( 2x + 3y ) + 1 ] [( 2 ( 2x + 3y ) - 1 ]

= ( 6x + 9y + 1 ) ( 4x + 6y - 1 )

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