Simplify: (3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)


(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)


To simplify, we will proceed as follows:

(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)

$=[(3 x+2 y)(4 x+3 y)]-[(2 x-y)(7 x-3 y)]$

$=[3 x(4 x+3 y)+2 y(4 x+3 y)]-[2 x(7 x-3 y)-y(7 x-3 y)]$                           (Distributive law)

$=12 x^{2}+9 x y+8 x y+6 y^{2}-\left[14 x^{2}-6 x y-7 x y+3 y^{2}\right]$ 

$=12 x^{2}+9 x y+8 x y+6 y^{2}-14 x^{2}+6 x y+7 x y-3 y^{2}$            (Rearranging)

$=12 x^{2}-14 x^{2}+9 x y+8 x y+6 x y+7 x y+6 y^{2}-3 y^{2}$           (Combining like terms)

$=-2 x^{2}+30 x y+3 y^{2}$ 

Thus, the answer is $-2 x^{2}+30 x y+3 y^{2}$.



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