Question
Simplify: $(3x + 2y)(4x + 3y) - (2x - y)(7x - 3y)$
✓
Answer
To simplify, we will proceed as follows:
$ (3 x+2 y)(4 x+3 y)-(2 x-y)(7 x-3 y) $
$ =[(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)] \text { (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 $
$ =12 x^2-14 x^2+9 x y+8 x y+6 x y+7 x y+6 y^2-3 y^2 $
$ =-2 x^2+30 x y+3 y^2 \text { (Rearranging) }$
Thus, the answer is $-2 x^2+30 x y+3 y^2$.
$ (3 x+2 y)(4 x+3 y)-(2 x-y)(7 x-3 y) $
$ =[(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)] \text { (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 $
$ =12 x^2-14 x^2+9 x y+8 x y+6 x y+7 x y+6 y^2-3 y^2 $
$ =-2 x^2+30 x y+3 y^2 \text { (Rearranging) }$
Thus, the answer is $-2 x^2+30 x y+3 y^2$.
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