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#)Giải :
\(x^2-y^2+3x-3y=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\)
\(x^2-y^2+3x-3y\)
\(=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)\)
\(=\left(x-y\right)\left(x+x+3\right)\)
~ Rất vui vì giúp đc bn ~
=(x^2-2xy+y^2)-(3x-3y)+2
=(x-y)^2-3(x-y)+2
=(x-y-2)(x-y-1)
\(-y^2+2xy-x^2+3x-3y\)
\(=-\left(x^2-2xy+y^2\right)+3\left(x-y\right)\)
\(=-\left(x-y\right)^2+3\left(x-y\right)\)
\(=\left(x-y\right)\left(-x+y+3\right)\)
\(=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y+3\right)\)
\(=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)=\left(x-y\right)\left(x+y+3\right)\)
1)
=3(x-y)+(x-y)(x+y)
=(x-y)(3x+3y)
2)
=x^2+2x+x+2
=x(x+2)+x+2
=(x+1)(x+2).
\(3x-3y+x^2-y^2\)
\(=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(3+x+y\right)\)
\(x^2+3x+2\)
\(=x^2+2x+x+2\)
\(=x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+1\right)\left(x+2\right)\)
Bài làm :
\(\text{a)}9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)
\(\text{b)}3x^4y^2+3x^3y^2+3xy^2+3y^2\)
\(=\left(3x^4y^2+3xy^2\right)+\left(3x^3y^2+3y^2\right)\)
\(=3xy^2\left(x^3+1\right)+3y^2\left(x^3+1\right)\)
\(=\left(3xy^2+3y^2\right)\left(x^3+1\right)\)
\(=3y^2\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)
\(\text{c)}\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)
\(=\left(x+y-1\right)\left(x^2+x+y^2+y+1-xy\right)\)
\(d ) x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
=(x+y)(x-y)+3(x+y)=(x+y)(x-y+3)
=(x+y)(x-y)+3(x+y)=(x+y)(x-y+3)