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a) (x - y)(x + y + 3). b) (x + y - 2xy)(2 + y + 2xy).
c) x 2 (x + l)( x 3 - x 2 + 2). d) (x – 1 - y)[ ( x - 1 ) 2 + ( x - 1 ) y + y 2 ].
\(1,\\ a,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\\ b,=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\\ c,=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\\ d,=x\left(x-2y\right)+t\left(x-2y\right)=\left(x+t\right)\left(x-2y\right)\\ 2,\\ \Rightarrow x^2-4x+4-x^2+9=6\\ \Rightarrow-4x=-7\Rightarrow x=\dfrac{7}{4}\\ 3,\\ a,x^2+2x+2=\left(x+1\right)^2+1\ge1>0\\ b,-x^2+4x-5=-\left(x-2\right)^2-1\le-1< 0\)
a) \(=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
\(=\left(x-1\right)^2\left(x^2+x+1\right)\)
b) \(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
c) Đổi đề: \(a^2x+a^2y-7x-7y\)
\(=a^2\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(a^2-7\right)\)
d) \(=x^2\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x^2+y\right)\)
e) \(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
g) \(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h) \(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)
i) \(=\left(x+1\right)^2-4=\left(x+1-2\right)\left(x+1+2\right)=\left(x-1\right)\left(x+3\right)\)
a\(x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
b)\(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
d)\(=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(x^2+y\right)\left(x-b\right)\)
e)\(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
g)\(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h)\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)
i)\(=\left(x-1\right)^2-4=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\)
a) (5x - 3y)(x - 3y)(x + 3y).
b) 3(a – b + c) ( x + 6 y ) 2 .
c) (x-y-2m + n)(x-y + 2m-n)
\(8x^3+12x^2y+6xy^2+y^3-z^3\)
\(=\left(2x+y\right)^3-z^3\)
\(=\left(2x+y-z\right)\left[4x^2+z\left(2x+y\right)+z^2\right]\)
a, 8a3 - 36a2 +54ab2 - 27b3
=(8a3-36a2b +54ab2 - 27b3)
=(2a-3b)2
=(2a-3b)(2a-3b)(2a-3b)
b, 8x3 + 12x2y + 6xy2 + y3 - z 3
=(8x3 + 12x2y + 6xy2 + y3) - z3
=(2x + y)3 - y3
=(2x + y +z) . [ (2x + Y)2 + 2(2x + y)+ z2
= (2x + y + z)(4x2 + 4xy + y2 + 4x + 2y + z2
a) \(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
a) Ta có: \(x^4+2x^3-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)
h) \(y\left(y-x\right)^3-x\left(x-y\right)^2+xy\left(x-y\right)=y\left(y-x\right)^3-x\left(y-x\right)^2-xy\left(y-x\right)=\left(y-x\right)\left[y\left(y-x\right)^2-x-xy\right]=\left(y-x\right)\left[y\left(y^2-2xy+x^2\right)-x-xy\right]=\left(y-x\right)\left(y^3-2xy^2+x^2y-x-xy\right)\)
i) \(10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(2b-a\right)^2=10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(a-2b\right)^2=\left(a-2b\right)^2\left(10x^2-x^2-2\right)=\left(a-2b\right)^2\left(9x^2-2\right)\)
a, 4\(x^3\).y + \(\dfrac{1}{2}\)yz
=y.(4\(x^3\) + \(\dfrac{1}{2}\)z)
b, (a2 + b2 - 5)2 - 2.(ab + 2)2
= [a2 + b2 - 5 - \(\sqrt{2}\)(ab + 2) ].[ a2 + b2 - 5 + \(\sqrt{2}\)(ab +2)]
a) \(4x^3y+\dfrac{1}{2}yz=y\left(4x^3+\dfrac{1}{2}z\right)\)
b) \(\left(a^2+b^2-5\right)^2-2.\left(ab+2\right)^2\)
\(=\left[\left(a^2+b^2-5\right)+2\left(ab+2\right)\right]\left[\left(a^2+b^2-5\right)-2\left(ab+2\right)\right]\)
\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)
\(=\left[a^2+b^2+2ab-1\right]\left[a^2+b^2-2ab-9\right]\)
\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)
\(=\left[\left(a+b+1\right)\left(a+b-1\right)\right]\left[\left(a-b+3\right)\left(a-b-3\right)\right]\)
1) \(x^2\left(a-b\right)m-2xy\left(a-b\right)+ay^2-by^2=\left(a-b\right)x^2m-\left(a-b\right)2xy+\left(a-b\right)y^2=\left(a-b\right)\left(x^2m-2xy+y^2\right)\)
2) \(10a^3-10a=10a\left(a^2-1\right)=10a\left(a+1\right)\left(a-1\right)\)
3) \(16a^3xy-54b^3xy^4=2xy\left(8a^3-27b^3y^3\right)=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)
4) \(16+2x^3y^3=2\left(8+x^3y^3\right)=2\left(2+xy\right)\left(4+2xy+x^2y^2\right)\)
5) \(\left(a+b\right)^3+c^3=\left(a+b+c\right)\left(\left(a+b\right)^2+\left(a+b\right)c+c^2\right)=\left(a+b+c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)