1.

Factorise `(2x+3y)^(2)+14(2x+3y)(3x-y)-32(3x-y)^(2)`.

Answer» Let 2x+3y=a and 3x-y=b
`therefore` Given expression : `(2x+3y)^(2)+14(2x+3y)(3x-y)-32(3x-y)^(2)`
`=a^(2)+14ab-32b^(2)=a^(2)+(16-2)ab-32b^(2)`
`=a^(2)+16ab-2ab-32b^(2)=a(A+16b)-2b(a+16b)`
=(a+16b)(a-2b)
=[(2x+3y)+16(3x-y)][(2x+3y)-2(3x-y)]
=(2x+3y+48x-16y)(2x+3y-6x+22y)
=(50x-13y)(-4x+5y)=(50x-13y)(5y-4x)


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