Phân tích các đa thức thành nhân tử
1,7x - 7xy - 5x + 5y.
2, x + 4x + 3
3,2x - 7x + 5
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![](https://rs.olm.vn/images/avt/0.png?1311)
`a)7x^3y^2+14x^2y^3+7xy^4`
`=7xy^2(x^2+2xy+y^2)`
`=7xy^2(x+y)^2`
______________________________________________
`b)x^2-xy+5x-5y`
`=x(x-y)+5(x-y)`
`=(x-y)(x+5)`
______________________________________________
`c)3x^2-6xy-12+3y^2`
`=3(x^2-2xy-4+y^2)`
`=3[(x-y)^2-4]`
`=3(x-y-2)(x-y+2)`
a)7x3y2+14x2y3+7xy4
=7xy2(x2+2xy+y2)
=7xy2(x+y)2
b)x2-xy + 5x - 5y
=x(x-y) + 5(x-y)
=(x-y) (x+5)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(39x-39y=39\left(x-y\right)\)
b) \(3x^2\left(x-3y\right)-5y\left(3y-x\right)=3x^2\left(x-3y\right)+5y\left(x-3y\right)\)
\(=\left(3x^2+5x\right)\left(x-3y\right)=x\left(3x+5\right)\left(x-3y\right)\)
c) \(16x^2+24xy+9y^2=\left(4x\right)^2+4x.3y.2+\left(3y\right)^2=\left(4x+3y\right)^2\)
d) \(25x^2-\frac{1}{25y^2}=\left(5x\right)^2-\left(\frac{1}{5y}\right)^2=\left(5x-\frac{1}{5y}\right)\left(5x+\frac{1}{5y}\right)\)
e) \(7x^2-7xy+5x-5y=7x\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(7x+5\right)\)
f) \(5x^2-45y^2-30y-5=5\left(x^2-9y^2-6y-1\right)=5\left[x^2-\left(9y^2+6y+1\right)\right]\)
\(=5\left[x^2-\left(3y+1\right)^2\right]=5\left(x-3y-1\right)\left(x+3y+1\right)\)
g) \(x^2+2x+1-y^2-4y-1=\left(x^2+2x+1\right)-\left(y^2+2y+1\right)\) ( Chắc đề vậy :v )
\(=\left(x+1\right)^2-\left(y+1\right)^2=\left(x+1-y-1\right)\left(x+1+y+1\right)=\left(x-y\right)\left(x+y+2\right)\)
h) \(4x^2+8x-5=4x^2-2x+10x-5=2x\left(2x-1\right)+5\left(2x-1\right)\)
\(=\left(2x-1\right)\left(2x+5\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Vô đây xem: bài 1:phân tích đa thức thành nhân tửa)7x^3y-14x^2y+7xy^3b)3x^2-3xy-5x+5yc)x^2+7x+12giúp mình với - Hoc24
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,=7xy\left(x^2-2xy+y^2\right)=7xy\left(x-y\right)^2\\ b,=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\\ c,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a/ (5x^2 -10xy+5y^2)-20z^2=5[(x-y)^2-(2z)^2]=5(x-y-2x)(x-y+2z)
b/16x-5x^2-3=-[5x^2-16x+3]=-[(5x^2-x)-(15x+3)]=-[x(5x-1)-3(5x-1)]=(3-x)(5x-1)
c/x^2+4x+3=(x^2+x)+(3x+3)=x(x+1)+3(x+1)=(x+1)(x+3)
2a/ 5x(X^2-9)=0=>x=0 hoặc x^2=9=>x=0 hoặc x=+-3
b/x^2-7x+10=0=>(x^2-2x)-(5x-10)=0=>x(x-2)-5(x-2)=0=>x-2=0 hoặc x-5 =0 => tự tính nhé!
Answer:
Bài 1:
\(5x² - 10xy + 5y² - 20z²\)
\(= 5( x² - 2xy + y² - 4z²)\)
\(= 5 [(x² - 2xy + y²) - (2z)²]\)
\(= 5 [(x - y)² - (2z)²]\)
\(= 5 (x - y - 2z) ( x - y + 2z)\)
\(16x - 5x² - 3 \)
\(= -( 5x² - 16x + 3)\)
\(= -( 5x² - 15x - 1x + 3)\)
\(= - [ (5x² -x) - (15x -3)]\)
\(= - [ x(5x -1) -3(5x -1)]\)
\(= - (5x-1)(x-3)\)
\(x² + 4x + 3\)
\(= x² + x + 3x + 3\)
\(= (x² + x) + (3x + 3)\)
\(= x( x + 1) +3 (x+1)\)
\(= (x+1) (x+3)\)
Bài 2:
\(5x\left(x^2-9\right)=0\)
\(\Rightarrow5x\left(x-3\right)\left(x+3\right)=0\)
Trường hợp 1: \(5x=0\Leftrightarrow x=0\)
Trường hợp 2: \(x-3=0\Leftrightarrow x=3\)
Trường hợp 3: \(x+3=0\Leftrightarrow x=-3\)
\(x^2-7x+10=0\)
\(\Rightarrow x^2-5x-2x+10=0\)
\(\Rightarrow x\left(x-5\right)-2\left(x-5\right)=0\)
\(\Rightarrow\left(x-5\right)\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-5=0\\x-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=2\end{cases}}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) (x^2+2xy+y^2)-9=(x+y)^2-9=(x+y-3)(x+y+3)
b) 5(x^2-2xy+y^2-4z^2)=5[(x-y)^2-4z^2]=5[(x-y-2z)(x-y+2z)
c)x^2-2x-5x+10=x(x-2)-5(x-2)=(x-5)(x-2)
d)2x^2-4x-3x+6=2x(x-2)-3(x-2)=(2x-3)(x-2)
2: x^2+4x+3
=x^2+3x+x+3
=(x+3)(x+1)
3: 2x^2-7x+5
=2x^2-2x-5x+5
=(x-1)(2x-5)