2: \(2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(5y-15\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
4: \(7x^3y-3xyz-21x^2+9z\)
\(=\left(7x^3y-21x^2\right)-\left(3xyz-9z\right)\)
\(=7x^2\left(xy-3\right)-3z\left(xy-3\right)\)
\(=\left(xy-3\right)\left(7x^2-3z\right)\)
6: \(9x^2-25y^2-6x+10y\)
\(=\left(9x^2-25y^2\right)-\left(6x-10y\right)\)
\(=\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y-2\right)\)
8: \(x^2y+xy+x+1\)
\(=\left(x^2y+xy\right)+\left(x+1\right)\)
\(=xy\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(xy+1\right)\)
10: \(x^2-\left(a+b\right)x+ab\)
\(=x^2-ax-bx+ab\)
\(=\left(x^2-ax\right)-\left(bx-ab\right)\)
\(=x\left(x-a\right)-b\left(x-a\right)\)
\(=\left(x-a\right)\left(x-b\right)\)
12: \(ax^2+ay-bx^2-by\)
\(=\left(ax^2-bx^2\right)+\left(ay-by\right)\)
\(=x^2\left(a-b\right)+y\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2+y\right)\)
14: \(x^2+x-ax-a\)
\(=\left(x^2+x\right)-\left(ax+a\right)\)
\(=x\left(x+1\right)-a\left(x+1\right)\)
\(=\left(x+1\right)\left(x-a\right)\)
16: \(2xy-ax+x^2-2ay\)
\(=\left(x^2+2xy\right)-\left(ax+2ay\right)\)
\(=x\left(x+2y\right)-a\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-a\right)\)
18: \(x^2y^2+y^3+zx^2+yz\)
\(=\left(x^2y^2+y^3\right)+\left(zx^2+yz\right)\)
\(=y^2\left(x^2+y\right)+z\left(x^2+y\right)\)
\(=\left(x^2+y\right)\left(y^2+z\right)\)
20: \(x^4+2x^3-4x-4\)
\(=\left(x^4-4\right)+\left(2x^3-4x\right)\)
\(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2+2x\right)\)
22: \(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-\left(x-y\right)\left(2x-2y\right)\)
\(=3\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(2x-2y\right)\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
24: \(x^2-y^2-2x-2y\)
\(=\left(x^2-y^2\right)-\left(2x+2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
2) $2xy-15-6x+5y$
$=(2xy-6x)+(5y-15)$
$=2x(y-3)+5(y-3)$
$=(y-3)(2x+5)$
4) $7x^3y-3xyz-21x^2+9z$
$=(7x^3y-21x^2)-(3xyz-9z)$
$=7x^2(xy-3)-3z(xy-3)$
$=(xy-3)(7x^2-3z)$
6) $9x^2-25y^2-6x+10y$
$=(9x^2-25y^2)-(6x-10y)$
$=[(3x)^2-(5y)^2]-2(3x-5y)$
$=(3x-5y)(3x+5y)-2(3x-5y)$
$=(3x-5y)(3x+5y-2)$
8) $x^2y+xy+x+1$
$=(x^2y+xy)+(x+1)$
$=xy(x+1)+(x+1)$
$=(x+1)(xy+1)$
10) $x^2-(a+b)x+ab$
$=x^2-ax-bx+ab$
$=(x^2-ax)-(bx-ab)$
$=x(x-a)-b(x-a)$
$=(x-a)(x-b)$
12) $ax^2+ay-bx^2-by$
$=(ax^2 +ay)-(bx^2+by)$
$=a(x^2+y)-b(x^2+y)$
$=(x^2+y)(a-b)$
14) $x^2+x-ax-a$
$=(x^2+x)-(ax+a)$
$=x(x+1)-a(x+1)$
$=(x+1)(x-a)$
16) $2xy-ax+x^2-2ay$
$=(x^2-ax)+(2xy-2ay)$
$=x(x-a)+2y(x-a)$
$=(x-a)(x+2y)$
18) $x^2y^2+y^3+zx^2+yz$
$=(x^2y^2+y^3)+(zx^2+yz)$
$=y^2(x^2+y)+z(x^2+y)$
$=(x^2+y)(y^2+z)$
20) $x^4+2x^3-4x-4$
$=(x^4-4)+(2x^3-4x)$
$=[(x^2)^2-2^2]+2x(x^2-2)$
$=(x^2-2)(x^2+2)+2x(x^2-2)$
$=(x^2-2)(x^2+2+2x)$
22) $3x^2-3y^2-2(x-y)^2$
$=(3x^2-3y^2)-2(x-y)^2$
$=3(x^2-y^2)-2(x-y)^2$
$=3(x-y)(x+y)-2(x-y)^2$
$=(x-y)[3(x+y)-2(x-y)]$
$=(x-y)(3x+3y-2x+2y)$
$=(x-y)(x+5y)$
24) $x^2-y^2-2x-2y$
$=(x^2-y^2)-(2x+2y)$
$=(x-y)(x+y)-2(x+y)$
$=(x+y)(x-y-2)$
$\text{#}Toru$
