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a) 4x2-5xy+y2
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DL
1
3 tháng 8 2021
a) \(4x^2-9y^2+6x-9y\)
\(=\left(2x-3y\right)\left(2x+3y\right)+3\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+3\right)\)
b) \(1-2x+2yz+x^2-y^2-z^2\)
\(=\left(x^2-2x+1\right)-\left(y^2-2yz+z^2\right)\)
\(=\left(x-1\right)^2-\left(y-z\right)^2\)
\(=\left(x-y+z-1\right)\left(x+y-z-1\right)\)
Tick hộ mình nha 😘
CD
1
22 tháng 11 2023
a: \(3abc^3-6a^2b^3c+12a^3bc\)
\(=3abc\cdot c^2-3abc\cdot2ab^2+3abc\cdot4a^2\)
\(=3abc\left(c^2-2ab^2+4a^2\right)\)
b: \(27-8y^3\)
\(=3^3-\left(2y\right)^3\)
\(=\left(3-2y\right)\left(9+6y+4y^2\right)\)
c: Sửa đề: \(4x^2+4x-y^2+1\)
\(=\left(4x^2+4x+1\right)-y^2\)
\(=\left(2x+1\right)^2-y^2\)
\(=\left(2x+1+y\right)\left(2x+1-y\right)\)
d: \(3a^2\cdot\left(x-2\right)-6ab\cdot\left(2-x\right)\)
\(=3a^2\cdot\left(x-2\right)+6ab\cdot\left(x-2\right)\)
\(=\left(x-2\right)\left(3a^2+6ab\right)\)
\(=3a\left(a+2b\right)\left(x-2\right)\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
4 tháng 11 2023
Bài 1:
\(a,2x^2y\left(2x^2y^2-xy^2\right)\\ =2x^2x^2y^2y-2x^2x.y^2.y=2x^4y^3-2x^3y^3\\ b,\left(x-1\right)\left(2x+3\right)\\ =x.2x+x.3-1.2x-1.3=2x^2+3x-2x-3\\ =2x^2+x-3\\ c,\left(20x^3y^4+10x^2y^3-5xy\right):5xy\\ =20x^3y^4:5xy+10x^2y^3:5xy-5xy:5xy\\ =\left(20:5\right).\left(x^3:x\right).\left(y^4:y\right)+\left(10:5\right).\left(x^2:x\right).\left(y^3:y\right)-\left(5:5\right).\left(x:x\right).\left(y:y\right)\\ =4x^2y^3+2xy^2-1\\ d,\left(y-3x\right)^2-\left(y^2-6xy\right)\\ =\left[y^2-2.y.3x+\left(3x\right)^2\right]-\left(y^2-6xy\right)\\ =y^2-6xy+9x^2-y^2+6xy =9x^2\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
4 tháng 11 2023
Bài 2:
\(a,4xy+4xz=4x\left(y+z\right)\\ b,x^2-y^2+9-6x\\ =\left(x^2-6x+9\right)-y^2\\ =\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\left(x-3+y\right)\)
Bài 3:
\(a,\dfrac{3xy}{y+z}+\dfrac{3xz}{y+z}\\=\dfrac{3xy+3xz}{y+z}\\ =\dfrac{3x\left(y+z\right)}{\left(y+z\right)}=3x\left(Với:y\ne-z\right)\\ b,\dfrac{x}{x+2}-\dfrac{x}{x-2}\\ =\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}\\ =\dfrac{x^2-2x-x^2-2x}{\left(x+2\right)\left(x-2\right)}=0\)
18 tháng 7 2021
e) Ta có: \(x^4-2x^3+2x-1\)
\(=\left(x^4-1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2+1\right)\left(x-1\right)\left(x+1\right)-2x\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\cdot\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\cdot\left(x-1\right)^3\)
h) Ta có: \(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
18 tháng 7 2021
a) Ta có: \(x^2-y^2-2x-2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
b) Ta có: \(x^2\left(x+2y\right)-x-2y\)
\(=\left(x+2y\right)\left(x^2-1\right)\)
\(=\left(x+2y\right)\left(x-1\right)\left(x+1\right)\)
ML
2
26 tháng 8 2021
\(A=x^2-y^2+7x+7y\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(B=4x^3-4x^2+x\)
\(=x\left(4x^2-4x+1\right)\)
\(=x\left(2x-1\right)^2\)
\(C=x^2-6xy+9y^2-9\)
\(=\left(x-3y\right)^2-9\)
\(=\left(x-3y-3\right)\left(x-3y+3\right)\)
26 tháng 8 2021
A=\(x^2+7x+7y-y^2=\left(x^2-y^2\right)+\left(7x+7y\right)=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)=\left(x+y\right)\left(x-y+7\right)\)
B=\(4x^3-4x^2+x=x\left(4x^2-4x+1\right)=x\left(2x-1\right)^2\)
C=\(x^2+9y^2-9-6xy=\left(x^2-6xy+9y^2\right)-9=\left(x-3y\right)^2-3^2=\left(x-3y-3\right)\left(x-3y+3\right)\)
TA
2 tháng 8 2021
`9-x^2-2xy-y^2`
`=9-(x^2+2xy+y^2)`
`=3^2-(x+y)^2`
`=(3+x+y)(3-x-y)`
\(4x^2-5xy+y^2=\left(4x^2-5xy+\dfrac{25}{16}y^2\right)-\dfrac{9}{16}y^2=\left(2x-\dfrac{5}{4}y\right)^2-\dfrac{9}{16}y^2=\left(2x-\dfrac{5}{4}y-\dfrac{3}{4}y\right)\left(2x-\dfrac{5}{4}y+\dfrac{3}{4}y\right)=\left(2x-2y\right)\left(2x-\dfrac{1}{2}y\right)=\left(x-y\right)\left(4x-y\right)\)
\(4x^2-5xy+y^2\)
\(=4x^2-4xy-xy+y^2\)
\(=4x\left(x-y\right)-y\left(x-y\right)\)
\(=\left(x-y\right)\left(4x-y\right)\)