Phân tích các đa thức sau thành nhân tử:
a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
b) \(3\left(x-y\right)-5x\left(y-x\right)\)
phân tích đa thức sau thành nhân tử
a.\(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
b.\(3\left(x-y\right)-5x\left(y-x\right)\)
a.
\(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
b.
\(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(a,5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
\(b,3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
Chúc bạn học tốt!
a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=\left(x-2y\right)\left(5x^2-15x\right)=\left(x-2y\right)5x\left(x-3\right).\)
\(b.3\left(x-y\right)-5\left(y-x\right)=3\left(x-y\right)+5\left(x-y\right)\)
\(=\left(3+5\right)\left(x-y\right)=8\left(x-y\right)\)
Bài 1: Phân tích đa thức thành nhân tử:
1) \(3x^3y^2-6xy\)
2) \(\left(x-2y\right).\left(x+3y\right)-2.\left(x-2y\right)\)
3) \(\left(3x-1\right).\left(x-2y\right)-5x.\left(2y-x\right)\)
4) \(x^2-y^2-6y-9\)
5) \(\left(3x-y\right)^2-4y^2\)
6) \(4x^2-9y^2-4x+1\)
8) \(x^2y-xy^2-2x+2y\)
9) \(x^2-y^2-2x+2y\)
Bài 2: Tìm x:
1) \(\left(2x-1\right)^2-4.\left(2x-1\right)=0\)
2) \(9x^3-x=0\)
3) \(\left(3-2x\right)^2-2.\left(2x-3\right)=0\)
4) \(\left(2x-5\right)\left(x+5\right)-10x+25=0\)
Bài 2:
1: \(\left(2x-1\right)^2-4\left(2x-1\right)=0\)
=>\(\left(2x-1\right)\left(2x-1-4\right)=0\)
=>(2x-1)(2x-5)=0
=>\(\left[{}\begin{matrix}2x-1=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)
2: \(9x^3-x=0\)
=>\(x\left(9x^2-1\right)=0\)
=>x(3x-1)(3x+1)=0
=>\(\left[{}\begin{matrix}x=0\\3x-1=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\end{matrix}\right.\)
3: \(\left(3-2x\right)^2-2\left(2x-3\right)=0\)
=>\(\left(2x-3\right)^2-2\left(2x-3\right)=0\)
=>(2x-3)(2x-3-2)=0
=>(2x-3)(2x-5)=0
=>\(\left[{}\begin{matrix}2x-3=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)
4: \(\left(2x-5\right)\left(x+5\right)-10x+25=0\)
=>\(2x^2+10x-5x-25-10x+25=0\)
=>\(2x^2-5x=0\)
=>\(x\left(2x-5\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{2}\end{matrix}\right.\)
Bài 1:
1: \(3x^3y^2-6xy\)
\(=3xy\cdot x^2y-3xy\cdot2\)
\(=3xy\left(x^2y-2\right)\)
2: \(\left(x-2y\right)\left(x+3y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\cdot\left(x+3y\right)-2\cdot\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+3y-2\right)\)
3: \(\left(3x-1\right)\left(x-2y\right)-5x\left(2y-x\right)\)
\(=\left(3x-1\right)\left(x-2y\right)+5x\left(x-2y\right)\)
\(=(x-2y)(3x-1+5x)\)
\(=\left(x-2y\right)\left(8x-1\right)\)
4: \(x^2-y^2-6y-9\)
\(=x^2-\left(y^2+6y+9\right)\)
\(=x^2-\left(y+3\right)^2\)
\(=\left(x-y-3\right)\left(x+y+3\right)\)
5: \(\left(3x-y\right)^2-4y^2\)
\(=\left(3x-y\right)^2-\left(2y\right)^2\)
\(=\left(3x-y-2y\right)\left(3x-y+2y\right)\)
\(=\left(3x-3y\right)\left(3x+y\right)\)
\(=3\left(x-y\right)\left(3x+y\right)\)
6: \(4x^2-9y^2-4x+1\)
\(=\left(4x^2-4x+1\right)-9y^2\)
\(=\left(2x-1\right)^2-\left(3y\right)^2\)
\(=\left(2x-1-3y\right)\left(2x-1+3y\right)\)
8: \(x^2y-xy^2-2x+2y\)
\(=xy\left(x-y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-2\right)\)
9: \(x^2-y^2-2x+2y\)
\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
Phân tích các đa thức sau thành nhân tử
a)\(5x\left(x-2y\right)+2\left(2y-x\right)^2\)
b)\(7x\left(y-4\right)^2-\left(4-y\right)^3\)
c)\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
Phân tích đa thức thành nhân tử
\(\left(9x+2y\right)^2+\left(7+2y\right)\left(7-2y\right)-x^2\)
\(\left(3x+4\right)^2+\left(4x-3\right)^2+\left(2+5x\right)\left(2-5x\right)\)
\(\left(5x+y\right)\left(25x^2-5xy+y^2\right)-\left(5x-y\right)\left(25x^2+5xy+y^2\right)\)
Answer:
Câu đầu bạn xem lại.
\(\left(3x+4\right)^2+\left(4x-3\right)^2+\left(2+5x\right).\left(2-5x\right)\)
\(=\left(3x\right)^2+2.2x.4+4^2+\left(4x\right)^2-2.4x.3+3^2+2^2-\left(5x\right)^2\)
\(=9x^2+24x+16+16x^2-24x+9+4-25x^2\)
\(=\left(9x^2+16x^2-25x^2\right)+\left(24x-24x\right)+\left(16+9+4\right)\)
\(=29\)
\(\left(5x+y\right).\left(25x^2-5xy+y^2\right)-\left(5x-y\right).\left(25x^2+5xy+y^2\right)\)
\(=\left(5x+y\right).[\left(5x\right)^2-5x.y+y^2]-\left(5x-y\right).[\left(5x\right)^2+5x.y+y^2]\)
\(=\left(5x\right)^3+y^3-[\left(5x\right)^3-y^3]\)
\(=\left(5x\right)^3+y^3-\left(5x\right)^3+y^3\)
\(=2y^3\)
Bài 1 : Phân tích đa thức thành nhân tử
\(a,5x\left(x-2y\right)+2\left(2y-x\right)^2\)
\(b,7x\left(y-4\right)^2-\left(4-x\right)^3\)
\(c,\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
Phân tích đa thức \(\dfrac{2}{5}x^2+5x^3+x^2y\) thành nhân tử
a. \(x^2\left(\dfrac{2}{5}+5x+y\right)\)
b. \(\dfrac{1}{5}x^2\left(2+25x+5y\right)\)
Cách phân tích nào đúng a hay b và GIẢI THÍCH VÌ SAO?
A. Cách B sai vì 5 : 2/5 thì ko thể nào = 25 đc.
Câu 14: Kết quả phân tích đa thức 5x3 - 10x2y + 5xy2 thành nhân tử là:
A. 5x(x – y)2 B. x(5x – y)2 C. -5x(x + y)2 D. x(x + 5y)2
Câu 15: Rút gọn phân thức:\(\dfrac{15x\left(3-y\right)}{45x\left(y-3\right)}\)ta được kết quả là:
A. 3 B. -3x C.\(\dfrac{1}{3x}\) D.\(\dfrac{-1}{3}\)
Phân tích đa thức thành nhân tử:
\(a,x^2-x\)
\(b,5x^2.\left(x-2y\right)-15x\left(x-2y\right)\)
\(c,3\left(x-y\right)-5x\left(y-x\right)\)
Câu a : \(x^2-x=x^2-\sqrt{x}^{^2}=\left(x-\sqrt{x}\right)\left(x+\sqrt{x}\right)\)
Câu b và câu c đều có nhân tử chung . Rồi tự làm nhé
Phân tích đa thức thành nhân tử
a) \(3\left(x-y\right)-5x\left(y-x\right)\)
b) \(x^3+2x^2y+xy^2-9x\)
c)\(14x^2y-21xy^2+28x^2y^2\)
a) 3( x - y ) - 5x( y - x )
= 3( x - y ) - 5x[ -( x - y ) ]
= 3( x - y ) + 5x( x - y )
= ( 3 + 5x )( x - y )
b) x3 + 2x2y + xy2 - 9x
= x( x2 + 2xy + y2 - 9 )
= x[ ( x + y )2 - 32 ]
= x( x + y - 3 )( x + y + 3 )
c) 14x2y - 21xy2 + 28x2y2
= 7xy( 2x - 3y + 4xy )
Bài giải
\(a,\text{ }3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(b,\text{ }x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y+3\right)\left(x+y-3\right)\)
\(c,\text{ }14x^2y-21xy^2+28x^2y\)
\(=7xy\left(2x-3y+4x\right)\)
\(=7xy\left(6x-3y\right)\)
a, \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(3+5x\right)\)
b, \(x^3+2x^2y+xy^2-9x=x\left(x+y+3\right)\left(x+y-3\right)\)
c, \(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)