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a, \(x^3-2x-y^3+2y\) (sửa đề)
\(=\left(x^3-y^3\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2-2\right)\)
b, \(\left(x-y\right)\left(x+y\right)-4zx+4yz\)
\(=\left(x-y\right)\left(x+y\right)-\left(4zx-4yz\right)\)
\(=\left(x-y\right)\left(x+y\right)-4z\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-4z\right)\)
Bạn xem lại đề câu a giúp mình nha!
a: \(a\left(x-y\right)-b\left(y-x\right)+c\left(x-y\right)\)
\(=a\left(x-y\right)+b\left(x-y\right)+c\left(x-y\right)\)
\(=\left(x-y\right)\left(a+b+c\right)\)
b: \(a^m-a^{m+2}\)
\(=a^m-a^m\cdot a^2\)
\(=a^m\left(1-a^2\right)\)
\(=a^m\left(1-a\right)\left(1+a\right)\)
\(\left(x+y\right)\left(x^2-y^2\right)+\left(y+z\right)\left(y^2-z^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=-y^3-xy^2+x^2y+x^3-z^3-yz^2+y^2z+y^3-x^3-zx^2+z^2x+z^3\)
\(=-xy^2+x^2y-yz^2+y^2z-zx^2+z^2x\)
\(=\left(x-y\right)\left(z-x\right)\left(z-y\right)\)
`#3107.101107`
`(4x - 1)^2 - 121`
`= (4x - 1)^2 - (11)^2`
`= (4x - 1 - 11)(4x - 1 + 11)`
`= (4x - 12)(4x + 10)`
`= 4(x - 3) * 2(2x + 5)`
`= 8(x - 3)(2x + 5)`
_____
`x^6 - y^6`
`= (x^3)^2 - (y^3)^2`
`= (x^3 - y^3)(x^3 + y^3)`
`= (x - y)(x^2 + xy + y^2)(x + y)(x^2 - xy + y^2)`
`= (x - y)(x + y)(x^2 + xy + y^2)`
____
Sử dụng các HĐT:
`@` `A^2 - B^2 = (A - B)(A + B)`
`@` `A^3 - B^3 = (A - B)(A^2 + AB + B^2)`
`@` `A^3 + B^3 = (A + B)(A^2 - AB + B^2).`
a: \(\left(4x-1\right)^2-121\)
\(=\left(4x-1\right)^2-11^2\)
\(=\left(4x-1-11\right)\left(4x-1+11\right)\)
\(=\left(4x-12\right)\left(4x+10\right)\)
\(=8\left(x-3\right)\left(2x+5\right)\)
b: \(x^6-y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
4x(x+y)(x+y+z)(x+z)+y2z2=4(x2+xy+xz)(x2+xy+xz+yz)+y2z2=4(x2+xy+xz)2+4yz(x2+xy+xz)+y2z2=(2(x2+xy+xz)+yz)2=(2x2+2xy+2xz+yz)
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: \(x^2-y^2-2x+2y\)
\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
(x+y)2-(x+y)-6
=(x+y)2+2.(x+y)-3.(x+y)-6
=(x+y)(x+y+2)-3.(x+y+2)
=(x+y+2)(x+y-3)