Phân tích thành nhân tử
( 1-x )2 + ( x-1 )( x-2 ) + ( 3-2x )( 3x-2)
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Những câu hỏi liên quan
18 tháng 8 2021
a: \(x\left(3x-2\right)-3x+2=\left(3x-2\right)\left(x-1\right)\)
b: \(3\left(x-y\right)-2x+2y=x-y\)
c: \(x\left(2x-1\right)-6x+3=\left(2x-1\right)\left(x-3\right)\)
4 tháng 12 2023
1: \(x\left(x-1\right)+\left(1+x\right)^2\)
\(=x^2-x+x^2+2x+1\)
\(=2x^2+x+1\)
Đa thức này ko phân tích được nha bạn
2: \(\left(x+1\right)^2-3\left(x+1\right)\)
\(=\left(x+1\right)\cdot\left(x+1\right)-\left(x+1\right)\cdot3\)
\(=\left(x+1\right)\left(x+1-3\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
3: \(2x\cdot\left(x-2\right)-\left(x-2\right)^2\)
\(=2x\left(x-2\right)-\left(x-2\right)\cdot\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)\)
4: \(3x\left(x-1\right)^2-\left(1-x\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^2\cdot\left(x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(3x+x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(4x-1\right)\)
5: \(3x\left(x+2\right)-5\left(x+2\right)^2\)
\(=\left(x+2\right)\cdot3x-\left(x+2\right)\cdot\left(5x+10\right)\)
\(=\left(x+2\right)\left(3x-5x-10\right)\)
\(=\left(-2x-10\right)\left(x+2\right)\)
\(=-2\left(x+5\right)\left(x+2\right)\)
6: \(4x\left(x-y\right)+3\left(y-x\right)^2\)
\(=4x\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\cdot4x+\left(x-y\right)\left(3x-3y\right)\)
\(=\left(x-y\right)\cdot\left(4x+3x-3y\right)\)
\(=\left(x-y\right)\left(7x-3y\right)\)
4 tháng 10 2018
\(x^2+8x-9\)
\(=x^2-x+9x-9\)
\(=x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x+9\right)\)
Câu đầu chưa học sorry
29 tháng 1 2024
a: \(x^2+2x+1+4x+4\)
\(=\left(x^2+2x+1\right)+\left(4x+4\right)\)
\(=\left(x+1\right)^2+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x+1+4\right)\)
\(=\left(x+1\right)\left(x+5\right)\)
b: Sửa đề: \(2x^3+6x^2+x^2+3x\)
\(=2x^2\left(x+3\right)+x\left(x+3\right)\)
\(=\left(x+3\right)\left(2x^2+x\right)\)
\(=x\left(x+3\right)\left(2x+1\right)\)
c: \(\dfrac{1}{2}x^2+\dfrac{1}{4}x+\dfrac{1}{4}x+1\)
\(=\dfrac{1}{4}x\left(\dfrac{1}{4}x+1\right)+\left(\dfrac{1}{4}x+1\right)\)
\(=\left(\dfrac{1}{4}x+1\right)\left(\dfrac{1}{4}x+1\right)=\left(\dfrac{1}{4}x+1\right)^2\)
17 tháng 7 2023
1) \(x\left(4x+1\right)\)
2) \(3\left(x-3y\right)\)
3) \(\left(2x+1\right)\left(2x+1+2\right)=\left(2x+1\right)\left(2x+3\right)\)
6 tháng 11 2021
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
15 tháng 7 2023
1)
a) \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)\)
\(=\left(x+2\right)\left[\left(x+2\right)-\left(x-2\right)\right]\)
\(=\left(x+2\right)\left(x+2-x+2\right)\)
\(=4\left(x+2\right)\)
b) \(x+2x^2+2x^3\)
\(=x\left(2x+2x^2+1\right)\)
15 tháng 7 2023
1) a. \(\left(x+2\right)\left(x+2-x+2\right)=4\left(x+2\right)\)
b. \(x\left(1+2x+2x^2\right)\)
2) a. \(=x^2-4-\left(x^2+4x+3\right)=x^2-4-x^2-4x-3=-4x-7\)
b. Áp dụng dạng \(\left(a+b\right)^2=a^2+b^2+2ab\)
\(\left(2x+1\right)^2+\left(3x-1\right)^2+2\left(2x+1\right)\left(3x-1\right)\)
\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)
YN
1 tháng 10 2021
a) \(x^3y^3+125=\left(xy\right)^3+5^3=\left(xy+5\right)\left(x^2y^2-5xy+25\right)\)
b) \(8x^3+y^3-6xy\left(2x+y\right)=\left(8x^3+y^3\right)-6xy\left(2x+y\right)=[\left(2x\right)^3+y^3]-6xy\left(2x+y\right)\)
\(=\left(2x+y\right)\left(4x^2-2xy+y^2\right)-6xy\left(2x+y\right)=\left(2x+y\right)\left(4x^2-2xy+y^2-6xy\right)\)
\(=\left(2x+y\right)\left(4x^2-8xy+y^2\right)\)
c) \(\left(3x+2\right)^2-2\left(x-1\right)\left(3x+2\right)+\left(x-1\right)^2\)
\(=[\left(3x+2\right)-\left(x-1\right)]^2=\left(3x+2-x+1\right)^2=\left(2x+3\right)^2=\left(2x+3\right)\left(2x+3\right)\)