Question

Factorise:12(a+1)^2 - 25(a+1)(b+2)+12(b+2)^2

Answer 1

Que :-

[12( a + 1)² - 25(a + 1)( b + 2) + 12(b + 2)²]

Solution:-

Let [ ( a + 1) = x ] and [ ( b + 2) = y ].

=) 12x² - 25xy + 12y²

Splitting [ 25xy as ( 16 + 9)xy ].

=) 12x² - ( 16 + 9 )xy + 12y²

=) 12x² - 16xy - 9xy + 12y²

=) 4x ( 3x - 4y ) - 3y ( 3x - 4y )

=) ( 3x - 4y) ( 4x - 3y )

Now,

Substituting the assumed value. we get,

=) [ 3(a + 1) - 4( b +2)] [ 4( a + 1) - 3( b +2)]

=) [ 3a + 3 - 4b - 8] [ 4a + 4 - 3b - 6 ]

=) [ 3a - 4b - 5 ] [ 4a - 3b - 2 ]

Identity Used:-

• ( a + b)² = a² + b² + 2ab