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\(1\hept{\begin{cases}6x^2-8x+3x-4\\2x\left(3x-4\right)+\left(3x-4\right)\\\left(3x-4\right)\left(2x+1\right)\end{cases}}\)
\(2\hept{\begin{cases}7x^2-7xy-5x+5y+6xy\\7x\left(x-y\right)-5\left(x-y\right)+\frac{6xy\left(x-y\right)}{\left(x-y\right)}\\\left(x-y\right)\left(7x-5+\frac{6xy}{\left(x-y\right)}\right)\end{cases}}\)
\(3\hept{\begin{cases}5x\left(x-y\right)-15\left(x-y\right)\\\left(x-y\right)\left(5x-15\right)\end{cases}}\)
\(4,,2x^2+x=x\left(2x+1\right)\)
\(5\hept{\begin{cases}x^3-4x-3x^2+12\\x\left(x^2-4\right)-3\left(x^2-4\right)\\\left(x+2\right)\left(x-2\right)\left(x-3\right)\end{cases}}\)
\(6\hept{\begin{cases}2x+2y+x^2-y^2\\2\left(x+y\right)+\left(x+y\right)\left(x-y\right)\\\left(x+y\right)\left(2+x-y\right)\end{cases}}\)
\(7\hept{\begin{cases}\left(x^2y-2xy\right)-\left(xy-2y\right)+\left(xy-y\right)\\xy\left(x-2\right)-y\left(x-2\right)+y\left(x-1\right)\\y\left(X-2\right)\left(x-1\right)+y\left(x-1\right)\end{cases}}\Leftrightarrow y\left(x-1\right)\left(x-2+1\right)\)
\(8\hept{\begin{cases}x\left(2-y\right)+z\left(2-y\right)\\\left(2-y\right)\left(x+1\right)\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1)
a) \(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right)\)
b) \(xz+yz-5\left(x+y\right)=z\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(z-5\right)\)
c) \(3x^2-3xy-5x+5y=\left(3x^2-3xy\right)-\left(5x-5y\right)=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
Bài 2:
a) \(x^2+4x-y^2+4=\left(x^2+2\cdot x\cdot2+2^2\right)-y^2=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)
b) \(3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-z\right)\left(x+y+z\right)\)
c) \(x^2-2xy+y^2-z^2+2zt-t^2=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1.\)
\(4x^2-12x+9\)
\(=\left(2x\right)^2-12x+3^2=\left(2x-3\right)^2\)
\(2.\)
\(7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(\left(7x-5\right)\left(x-y\right)\)
\(3.\)
\(x^3-9x\)
\(=x\left(x^2-9\right)\)
\(=x\left(x-3\right)\left(x+3\right)\)
\(4.\)
\(5x\left(x-y\right)-15\left(x-y\right)\)
\(=\left(5x-15\right)\left(x-y\right)\)
\(=5\left(x-3\right)\left(x-y\right)\)
\(5.\)
\(2x^2+x\)
\(=2x\left(x+1\right)\)
\(6.\)
\(x^3+27\)
\(=\left(x+3\right)\left(x^2-3x+9\right)\)
\(7.\)
\(2x^2-4xy+2y^2-32\)
\(=2\left(x^2-2xy+y^2-16\right)\)
\(=2\left[\left(x^2-2xy+y^2\right)-16\right]\)
\(=2\left[\left(x-y\right)^2-4^2\right]\)
\(=2\left(x-y+4\right)\left(x-y-4\right)\)
\(8.\)
\(x^3-4x-3x^2+12\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(9.\)
\(2x+2y+x^2-y^2\)
\(=2\left(x+y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+2\right)\)
\(10.\)
\(x^2y-2xy+y\)
\(=y\left(x^2-2x+1\right)\)
\(=y\left(x-1\right)^2\)
\(11.\)
\(y^2+2y\)
\(=y\left(y+2\right)\)
\(12.\)
\(y^2-x^2-6y-6x\)
\(=\left(y-x\right)\left(y+x\right)-6\left(y+x\right)\)
\(=\left(y+x\right)\left(y-x-6\right)\)
\(13.\)
\(x^3-3x\)
\(=x\left(x^2-3\right)\)
\(=x\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
\(14.\)
\(2x-xy+2z-yz\)
\(=x\left(2-y\right)+z\left(2-y\right)\)
\(=\left(2-y\right)\left(x+z\right)\)
Xong
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài giải:
a) x2 – xy + x – y = (x2 – xy) + (x - y)
= x(x - y) + (x -y)
= (x - y)(x + 1)
b) xz + yz – 5(x + y) = z(x + y) - 5(x + y)
= (x + y)(z - 5)
c) 3x2 – 3xy – 5x + 5y = (3x2 – 3xy) - (5x - 5y)
= 3x(x - y) -5(x - y) = (x - y)(3x - 5).
\(a) x^2 - xy+x-y\) \(= (x^2 - xy) + ( x- y) \)
\(=x(x-y) + (x-y)\)
\(= (x-y) (x+1)\)
\(b) xz + yz - 5(x+y)\) \(= (xz + yz) - 5(x+y)\)
\(= z(x+y) - 5(x+y)\)
\(= (x+y) (z-5)\)
\(c) 3x^2 - 3xy - 5x +5y = (3x^2-3xy) - (5x-5y)\)
\(= 3x(x-y) - 5(x-y)\)
\(= (x-y)(3x-5)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài nhiều quá... nhìn mik nổi gai ốc lun...oh my god sao mà nhiều vậy nè .
Mik định giải giúp bạn nhưng bây h mik hoảng quá ... nhiều vậy chắc mik chết mất... ToT ... >.< =)))
![](https://rs.olm.vn/images/avt/0.png?1311)
\(e,-5x+x^2-14\)
\(=x^2+2x-7x-14\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)
\(f,x^3+8+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+2x+4\right)+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+8x+4\right)\)
\(g,15x^2-7xy-2y^2\)
\(=15x^2+3xy-10xy-2y^2\)
\(=3\left(5x+y\right)-2y\left(5x+y\right)\)
\(=\left(5x+y\right)\left(3-2y\right)\)
\(h,3x^2-16x+5\)
\(=3x^2-x-15x+5\)
\(=x\left(3x-1\right)+5\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x+5\right)\)
\(a,x^3+2x^2y+xy^2=x\left(x^2+2xy+y^2\right)\)
\(=x\left(x+y\right)^2\)
\(b,4x^2-9y^2+4x-6y\)
\(=4x^2+4x+1-\left(9y^2+6y+1\right)\)
\(=\left(2x+1\right)^2-\left(3y+1\right)^2\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
\(c,-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left(y-x+5\right)\)
\(d,x^2+4x-12\)
\(=x^2-2x+6x-12\)
\(=x\left(x-2\right)+6\left(x-2\right)\)
\(=\left(x-2\right)\left(x+6\right)\)
13: =x(a^3-1)-b(a-1)
=x(a-1)(a^2+a+1)-b(a-1)
=(a-1)(a^2x+a*x+x-b)
12: =(x-y)(x+y)-(x-y)
=(x-y)(x+y-1)
10: =3(x^2-4y^2)
=3(x-2y)*(x+2y)
7: =x^2-x-5x+5=(x-1)(x-5)
8: =x^2+3x+4x+12=(x+3)(x+4)
9: =2x^2-6x-x+3=(x-3)(2x-1)