A.5x^2y^3-25x^3y^4+10x^3y^3
B.12x^2y-18xy^2-30y^2
C.5(x-y)-y(x-y)
D.y(x-z)+7(z-x)
E.27x^2(y-1)-9x^3(1-y)
F.36-12x+x^2
G.x^2+2xy+y^2-xz-yz
H.x^4+64
I.27x^2(y-1)-9x^3(1-y)
K.36-12x+x^2
M.-4x^2+4x-1
N.x^2+5x+6
P.x^2-x-6
Q.x^4-5x^2+4
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d)5.(x-y)-y(x-y)
=(x-y)(5-y)
e) y.(x-z)+7(z-x)
=y.(x-z)-7(x-z)
=(x-z)(y-7)
1, \(3x^2y^2-6x^2y^3+9x^2y^2\)
\(\Leftrightarrow12x^2y^2-6x^2y^2\)
\(\Leftrightarrow3x^2y^2\left(4+2y\right)\)
5x^2y^3 - 25x^3y^4 + 10x^3y^3
\(\Leftrightarrow5x^2y^3\left(1-5xy+2x\right)\)
a) \(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)
b) \(x^2-2x-15=\left(x^2-2x+1\right)-16=\left(x-1\right)^2-4^2=\left(x-1-4\right)\left(x-1+4\right)=\left(x-5\right)\left(x+3\right)\)
c) \(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
d) \(12x^2y-18xy^2-30y^2=6\left(2x^2y-3xy^2-5y^2\right)\)
e, ntc: x-y
f, đối dấu --> ntc
g, như ý f
h, \(36-12x+x^2=\left(6-x\right)^2=\left(x-6\right)^2\)
i, \(3x^3y^2-6x^2y^3+9x^2y^2=3x^2y^2\left(x-y+3\right)\)
a) \(5x^2y^3-25x^3y^4+10x^3y^3\)
\(=5x^2y^3\left(1-5xy+2x\right)\)
b) \(4x^2+12x+9\)
\(=\left(2x\right)^2+2.2x.3+3^2\)
\(=\left(2x+3\right)^2\)
c) \(11x+11y-x^2-xy\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(11-x\right)\)
d) \(27x^2\left(y-1\right)-9x^3\left(1-y\right)\)
\(=27x^2\left(y-1\right)+9x^3\left(y-1\right)\)
\(=\left(y-1\right)\left(27x^2+9x^3\right)\)
\(=9x^2\left(y-1\right)\left(3+x\right)\)
c/
\(11x+11y-x^2-xy\)
\(=\left(11x-x^2\right)+\left(11y-xy\right)\)
\(=x\left(11-x\right)+y\left(11-x\right)\)
= \(\left(11-x\right)\left(x+y\right)\)
\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
Đề câu g có vấn đề aa :>>>
Câu còn lại tương tự như trên mà
\(\left(x-1\right)^2-25\)
\(=x^2-2x+1-25\)
\(=x^2-2x-24\)
\(=x^2-6x+4x-24\)
\(=x.\left(x-6\right)+4.\left(x-6\right)\)
\(=\left(x+4\right).\left(x-6\right)\)
a, \(1-2y+y^2=\left(y+1\right)^2=\left(y+1\right)\left(y+1\right)\)
b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
c, \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
d, \(8-27x^3=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)