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xy+3x-7y=21
x(y+3)-7y+21=0
x(y+3)-7(y+3)=0
(y+3).(x-7)=0(còn lại tự làm ha)
\(a,=\left(xy-1-x-y\right)\left(xy-1+x+y\right)\\ b,Sửa:a^3+2a^2+2a+1\\ =a^3+a^2+a^2+a+a+1=\left(a+1\right)\left(a^2+a+1\right)\\ c,=1-4a^2-a\left(a^2-4\right)=1-4a^2-a^3+4a\\ =\left(1-a\right)\left(1+a+a^2\right)+4a\left(1-a\right)\\ =\left(1-a\right)\left(1+5a+a^2\right)\\ d,=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\\ =a^2\left(1-b\right)\left(1+b\right)+b\left(b-1\right)+a\left(b-1\right)\\ =\left(b-1\right)\left(-a^2-ab+b+a\right)\\ =\left(b-1\right)\left(b-1\right)\left(a+b\right)\left(1-a\right)\)
\(e,=x^2y+xy^2-yz\left(y+z\right)+x^2z-xz^2\\ =\left(x^2y+x^2z\right)+\left(xy^2-xz^2\right)-yz\left(y+z\right)\\ =x^2\left(y+z\right)+x\left(y-z\right)\left(y+z\right)-yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy-xz-yz\right)\\ =\left(y+z\right)\left(x+y\right)\left(x-z\right)\)
\(f,=xyz-xy-yz-xz+x+y+z-1\\ =xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(x-1\right)\\ =\left(z-1\right)\left(xy-y-x+1\right)=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)
b: \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)
\(=x^2y+xy^2-y^2z-yz^2+x^2z-xz^2\)
\(=x^2y-yz^2+xy^2-y^2z+x^2z-xz^2\)
\(=y\left(x-z\right)\left(x+z\right)+y^2\left(x-z\right)+xz\left(x-z\right)\)
\(=\left(x-z\right)\left(xy+yz+y^2+xz\right)\)
\(=\left(x-z\right)\left(x+y\right)\left(x+z\right)\)
a) a2 - bd - cd - ad + ab + ac = (a2 + ab + ac) - (ad + bd + cd) = a(a + b + c) - d(a + b + c) = (a - d)(a + b + c)
b) ab - 5b + 3a - 15 = b(a - 5) + 3(a - 5) = (b + 3)(a - 5)
c: Ta có: \(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
\(=a^4-2a^3b+2ab^3-b^4\)
\(=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)-2ab\left(a^2-b^2\right)\)
\(=\left(a-b\right)^3\cdot\left(a+b\right)\)
a, = -(xy+yz)+(xz+z^2) = (x+z).(z-y)
b, = (xy-7y)+(3x-21) = (x-7).(y+3)
c, = (ab-bc)+(ad-cd)+(a-c) = (a-c).(b+d-1)
d, = (ab+3a)-(2b+6) = (b+3).(a-2)
e, = (a^2-ab)-(ac-bc) = (a-b).(a-c)
Tk mk nha
a, -xy+xz-yz+z2 = -x(y-z)-z(y-z) = (-x-z)(y-z)
b, xy+3x-7y-21 = x(y+3)-7(y+3) = (x-7)(y+3)
c, ab-cd-bc+ad+a-c = (ab-bc)+(ad-cd)+(a-c) = b(a-c)+d(a-c)+(a-c) = (b+d+1)(a-c)
d, ab+3a-2b-6 = a(b+3)-2(b+3) = (a-2)(b+3)
e, a2 - ab - ac + bc = a(a - b) - c(a - b) = (a-c)(a-b)
f, ax+ay-2az = a(x+y-2z)