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a. \(2a^2+5ab-3b^2-7b-2\)
\(=\left(2a^2+6ab+2a\right)-\left(ab+3b^2+b\right)-\left(2a+6b+2\right)\)
\(=2a\left(a+3b+1\right)-b\left(a+3b+1\right)-2\left(a+3b+1\right)\)
\(=\left(2a-b-2\right)\left(a+3b+1\right)\)
b. \(2x^2-7xy+x+3y^2-3y\)
\(=\left(2x^2-xy\right)-\left(6xy-3y^2\right)+\left(x-3y\right)\)
\(=x\left(2x-y\right)-3y\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y+1\right)\)
c. \(6x^2-xy-2y^2+3x-2y\)
\(=\left(6x^2+3xy\right)-\left(4xy-2y^2\right)+\left(3x-2y\right)\)
\(=3x\left(2x+y\right)-2y\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y+1\right)\)
a\(x^2-3xy-2y^2 =x^2-xy-2xy-2y^2 =x(x-y)-2y(x-y) =(x-2y)(x-y)\)
1: \(=\left(x-3y\right)\left(x-y\right)-\left(x-3y\right)=\left(x-3y\right)\left(x-y-1\right)\)
4: \(=6x^2-4xy+3xy-2y^2+3x-2y\)
\(=\left(3x-2y\right)\left(2x+y\right)+3x-2y=\left(3x-2y\right)\left(2x+y+1\right)\)
a) \(x^2-x-xy-2y^2+2y\)
\(=x^2-x-2xy+xy-2y^2+2y\)
\(=\left(-2y^2-2xy+2y\right)+\left(xy+x^2-x\right)\)
\(=2y\left(-y-x+1\right)+x\left(y+x-1\right)\)
\(=-2y\left(y+x-1\right)+x\left(y+x-1\right)\)
\(=\left(x-2y\right)\left(y+x-1\right)\)
b) \(x^2+4xy+2x+3y^2+6y\)
\(=x^2+3xy+xy+2x+3y^2+6y\)
\(=\left(3y^2+3xy+6y\right)+\left(xy+x^2+2x\right)\)
\(=3y\left(y+x+2\right)+x\left(y+x+2\right)\)
\(=\left(3y+x\right)\left(y+x+2\right)\)
1/ \(2x^2+5xy+y^2=2\left(x^2+2x.\frac{5y}{4}+\frac{25y^2}{16}-\frac{17y^2}{16}\right)\)
\(=2\left[\left(x+\frac{5y}{4}\right)^2-\left(\frac{\sqrt{17}y}{4}\right)^2\right]=2\left(x+\frac{5-\sqrt{17}}{4}y\right)\left(x+\frac{5+\sqrt{17}}{4}y\right)\)
2/ \(x^2-3xy-2y^2=x^2-2x.\frac{3y}{2}+\frac{9y^2}{4}-\frac{17y^2}{4}\)
\(=\left(x-\frac{3y}{2}\right)^2-\left(\frac{\sqrt{17}y}{2}\right)^2=\left(x+\frac{-3-\sqrt{17}}{2}y\right)\left(x+\frac{-3+\sqrt{17}}{2}y\right)\)
3/ \(6x^2+xy-7x-2y^2+7y-5\)
\(=6x^2+4xy-10x-3xy-2y^2+5y+3x+2y-5\)
\(=2x\left(3x+2y-5\right)-y\left(3x+2y-5\right)+3x+2y-5\)
\(=\left(3x+2y-5\right)\left(2x-y+1\right)\)
4/ \(6a^2-ab-2b^2+a+4b-2\)
\(=6a^2-4ab+4a+3ab-2b^2+2b-3a+2b-2\)
\(=2a\left(3a-2b+2\right)+b\left(3a-2b+2\right)-\left(3a-2b+2\right)\)
\(=\left(3a-2b+2\right)\left(2a+b-1\right)\)