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1.(x+2y)^2-4(x-3y)^2

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1.(x+2y)^2-4(x-3y)^2
2.(2x-3y)^2-(2x+7y)^2
3.(x+y)^2-8(x+y-2)
4.x(a-b)^3-^y(b-a)^3
5.(3a+2b)^2-(a-b)^2
1.(x+2y)^2-4(x-3y)^2
1.(x+2y)^2-4(x-3y)^2
=(x+2y)^2-(2x-6y)^2
=(x+2y+2x-6y)(x+2y-2x+6y)
=(3x-4y)(8y-x)
2.(2x-3y)^2-(2x+7y)^2
=(2x-3y+2x+7y)(2x-3y-2x-7y)
=-10y(4x+4y)
=-40y(x+y)
3.(x+y)^2-8(x+y-2)
=(x+y)²-8(x+y)+16
=(x+y-4)²
4.x(a-b)^3-y(b-a)^3
=x(a-b)^3+y(a-b)^3
=(x+y)(a-b)^3
5.(3a+2b)^2-(a-b)^2
=(3a+2b+a-b)(3a+2b-a+b)
=(4a+b)(2a+3b)