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a) \(3xy^2-12xy+12x\)
\(=3x\left(y-4y+4\right)\)
b) \(3x^3y-6x^2y-3xy^3-6axy^2-3a^2xy+3xy\)
\(=3xy\left(x^2-2x-y^2-2ay-a^2+1\right)\)
\(=3xy\left[\left(x^2-2\cdot x\cdot1+1^2\right)-\left(y^2+2\cdot y\cdot a+a^2\right)\right]\)
\(=3xy\left[\left(x-1\right)^2-\left(y+a\right)^2\right]\)
\(=3xy\left(x-1-y-a\right)\left(x-1+y+a\right)\)
c) \(36-4a^2+20ab-25b^2\)
\(=6^2-\left[\left(2a\right)^2-2\cdot2a\cdot5b+\left(5b\right)^2\right]\)
\(=6^2-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
d) \(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)\)
\(=5a\left(a-b\right)^2-10\left(a-b\right)\)
\(=\left(a-b\right)\left[5a\left(a-b\right)-10\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(=5\left(a-b\right)\left(a^2-ab-2\right)\)
a. 3xy2-12xy+12x
= 3x(y2-4y+4)
= 3x(y-2)2
b. 3x3y-6x2y-3xy3-6axy2-3a2xy+3xy
= 3xy( x2-2x-y2-2ay-a2+1)
= 3xy ((x2-2x+1)-(a2-2ay-y2))
=3xy((x-1)2-(a-y)2)
= 3xy((x-1+a-y)(x-1-(a-y))
=3xy(x-1+a-y)(x-1-a+y)
d. =( 5a(a2-2ab+b2))-(10(a+b))
= 5a(a-b)2-10(a-b)
=5a(a-b)(a-b)-10(a-b)
=(a-b)(5a(a-b)-10)
Hình như mik làm sai hết rồi
\(x^2-2xy+y^2-a^2+4ab-4b^2\)
\(=\left(x-y\right)^2-\left(a-2b\right)^2\)
\(=\left(x-y-a+2b\right)\left(x-y+a-2b\right)\)
hk tốt
^^
4a2=4b2-4a+1
=(2a)2-2*2a*1+12-4b2= (2a-1)2-(2b)2(2a-1-2b)(2a-1+2b)
\(a.5a^3-10a^2b+5ab^2-10a+10b=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)=5a\left(a-b\right)^2-10\left(a-b\right)=5\left(a-b\right)\left(a^2-ab-2\right)\)
\(b.3x^3+6x^2y+3xy^2-12xz^2=3x\left(x^2+2xy+y^2-4z^2\right)=3x\left[\left(x+y\right)^2-4z^2\right]=3x\left(x+y+2z\right)\left(x+y-2z\right)\)
\(c.x^3+4xy^2-3x^2-6xy+4x^2y=x\left(x^2+4y^2-3x-6y+4xy\right)=4\left[\left(x+2y\right)^2-3\left(x+2y\right)\right]=4\left(x+2y\right)\left(x+2y-3\right)\)
\(d.12x^3-12x^2y+3xy^2-27xz^2=3x\left(4x^2-4xy+y^2-9z^2\right)=3x\left[\left(2x-y\right)^2-9z^2\right]=3x\left(2x-y-3z\right)\left(2x-y+3z\right)\)