Phân tích thành nhân tử: 5x(x – 1) – 3x(x – 1)
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11 tháng 10 2021
\(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)
\(=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)\)
\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)
L
1
Y
23 tháng 6 2023
\(\left(5x-10\right)\left(x^2-1\right)-\left(3x-6\right)\left(x^2-2x+1\right)\)
\(=\left(5x-10\right)\left(x-1\right)\left(x+1\right)-\left(3x-6\right)\left(x-1\right)^2\)
\(=\left(x-1\right)\left[\left(5x-10\right)\left(x+1\right)-\left(3x-6\right)\left(x-1\right)\right]\)
\(=\left(x-1\right)\left[5\left(x-2\right)\left(x+1\right)-3\left(x-2\right)\left(x-1\right)\right]\)
\(=\left(x-1\right)\left[\left(x-2\right)\left(5x+5-3x+3\right)\right]\)
\(=\left(x-1\right)\left[\left(x-2\right)\left(2x+8\right)\right]\)
\(=\left(x-1\right)\left(x-2\right)\left(2x+8\right)\)
27 tháng 7 2021
a) x2-x=x(x-1)
b) 3x-3y = 3(x-y)
c)3xy2+6xyz=3xy(y+2z)
d) 5x-20y=5(x-4y)
g) 5x(x-1)-(1-x)=5x(x-1)+(x-1)=(5x+1)(x-1)
27 tháng 7 2021
a, \(x^2-x=x\left(x-1\right)\)
b, \(3x-3y=3\left(x-y\right)\)
c, \(3xy^2+6xyz=3xy\left(y+2z\right)\)
d, \(5x-20y=5\left(x-4y\right)\)
g, \(5x\left(x-1\right)-\left(1-x\right)=\left(5x+1\right)\left(x-1\right)\)
NT
3
13 tháng 7 2016
\(5x\left(x-1\right)-3x\left(x-1\right)\)
\(=5x^2-5x-3x^2+3x\)
\(=2x^2-2x\)
\(=2x\left(x-1\right)\)
15 tháng 10 2021
Bài 2:
a: \(x^2+5x-6=\left(x+6\right)\left(x-1\right)\)
b: \(5x^2+5xy-x-y\)
\(=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-1\right)\)
c:\(-6x^2+7x-2\)
\(=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(-3x+2\right)\)
15 tháng 10 2021
1.
a) \(=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
b) \(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
c) \(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
2.
a) \(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
b) \(=5x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(5x-1\right)\)
c) \(=-\left[3x\left(2x-1\right)-2\left(2x-1\right)\right]=-\left(2x-1\right)\left(3x-2\right)\)
3.
b) \(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
c) \(=-\left[5x\left(x-3\right)-1\left(x-3\right)\right]=-\left(x-3\right)\left(5x-1\right)\)
4.
a) \(\Rightarrow\left(x-1\right)\left(5x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
b) \(\Rightarrow2\left(x+5\right)-x\left(x+5\right)=0\)
\(\Rightarrow\left(x+5\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
24 tháng 10 2021
\(a,=\left(x+y\right)\left(x+3\right)\\ b,=\left(x+2\right)\left(x+3\right)\)
H
21 tháng 8 2021
Phân tích đa thức thành nhân tử(tách hạng tử)
1)x^2+2x-3=x^2-x+3x-3=x(x-1)+3(x-1)=(x-1)(x+3)
2)x^2-5x+6=x^2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)
3)x^2+7x+12=(x+3)(x+4)
4)x^2-x-12=(x-4)(x+3)
5)3x^2+3x-36=3[(x-3)(x+4)]
6)5x^2-5x-10=5[(x-2)(x+1) ]
7)3x^2-7x-6=(x-3)(3x+2)
8)4x^2+4x-3=4x^2+6x-2x-3=(2x-1)(2x+3)
9)8x^2-2x-3=8x^2+4x-6x-3=(4x-3)(2x+1)
21 tháng 8 2021
1: \(x^2+2x-3=\left(x+3\right)\left(x-1\right)\)
2: \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
3: \(x^2+7x^2+12x=4x\left(2x+3\right)\)
4: \(x^2-x-12=\left(x-4\right)\left(x+3\right)\)
5: \(3x^2+3x-36=3\left(x^2+x-12\right)=3\left(x+4\right)\left(x-3\right)\)
6: \(5x^2-5x-10=5\left(x^2-x-2\right)=5\left(x-2\right)\left(x+1\right)\)
20 tháng 7 2021
a, \(\left(3x-6y\right)x+y\left(x-2y\right)=\left(3x+y\right)\left(x-2y\right)\)
b, \(3\left(x-y\right)-5x\left(y-x\right)=\left(3+5x\right)\left(x-y\right)\)
c, \(\dfrac{2}{5}x\left(y-1\right)+\dfrac{2}{5}y\left(1-y\right)=\left(\dfrac{2}{5}x-\dfrac{2}{5}y\right)\left(y-1\right)=\dfrac{2}{5}\left(x-y\right)\left(y-1\right)\)
d, \(x\left(x-1\right)-y\left(1-x\right)=\left(x+y\right)\left(x-1\right)\)
5x(x – 1) – 3x(x – 1) = x(x – 1)(5 – 3) = 2x(x – 1)