Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
Tìm x, y thuộc Z:
a) x^2+xy+y^2=2x+y
b) x^2+xy+y^2=x+y
c) x^2-3xy+3y^2=3y
d) x^2-2xy+5y^2=y+1
e) 3x-xy+y^2=3
f) 3x+317=5x^2
g) x^2=4^y+5
\(\dfrac{1}{3x-3y};\dfrac{1}{x^2-2xy+y^{ }2}\)
\(\dfrac{3}{x^2-3x};\dfrac{5}{2x-6}\)
\(\dfrac{x}{x+3};\dfrac{1}{3-x};\dfrac{1}{x^2-9}\)
\(\dfrac{1}{x^2+xy};\dfrac{1}{xy-ỳ^2};\dfrac{2}{y^2-x^2}\)
giúp với ạ :((
\(a,\dfrac{1}{3x-3y}=\dfrac{x-y}{3\left(x-y\right)^2};\dfrac{1}{x^2-2xy+y^2}=\dfrac{3}{3\left(x-y\right)^2}\\ b,\dfrac{3}{x^2-3x}=\dfrac{6}{2x\left(x-3\right)};\dfrac{5}{2x-6}=\dfrac{5x}{2x\left(x-3\right)}\\ c,\dfrac{x}{x+3}=\dfrac{x^2-3x}{\left(x-3\right)\left(x+3\right)};\dfrac{1}{3-x}=\dfrac{-x-3}{\left(x-3\right)\left(x+3\right)};\dfrac{1}{x^2-9}=\dfrac{1}{\left(x-3\right)\left(x+3\right)}\)
\(d,\dfrac{1}{x^2+xy}=\dfrac{xy-y^2}{xy\left(x+y\right)\left(x-y\right)};\dfrac{1}{xy-y^2}=\dfrac{x^2+xy}{xy\left(x-y\right)\left(x+y\right)};\dfrac{2}{y^2-x^2}=\dfrac{-2xy}{xy\left(x-y\right)\left(x+y\right)}\)
Bài 1: thực hiện phép tính
a, 2xy(x^2 + xy - 3y^2)
b, (x+2)(3x^2 - 4x)
c, (x^3 + 3x^2 - 8x - 20) : (x + 2)
d, (4x^2 - 4x - 4) : (x+4)
e, (2x^3 - 3x^2 + x - 2) : (x + 5)
f, (x+y)^2 + (x-y)^2 - 2(x+y)(x-y)
g, (a+b)^3 - (a-b)^3 - 2b^3
h, (x - y)(x + y)(x^2 + y^2)(x^4 + y^4)
i, 2x^2(x - 2) + 3x(x^2 - x - 2) - 5(3 - x^2)
k, (x - 1)(x - 3) - (4 - x)(2x + 1) - 3x^2 + 2x - 5
l, (x^4 - x^3 - 3x^2 + x + 2) : (x^2 - 1)
Phân tích đa thức thành nhân tử
X^4-1
2x-2xy-7x+7y
X^2-3x+xy-3y
X^2-xy+x-y
3x^2-16x+5
X^2-25+y^2-2xy
(X+y)-(x^2-y^2)
X^2-4x-y^2+4
2xy-x^2-y^2+16
X^2-2x-4y^2-4y
Tìm n;x;y
1: n chia hết cho 21 và n+1 chia hết cho 165
2: 5x-xy=26-3y
3: 3x+xy-4x=3
4: y2-5y+2x=xy-6
5: y2+3x-xy=6y-4
6: xy-y2=3y-x-5
7: (2x+5y+1).(2|x|+y+x2+x)=105
1)6x^2-12x
2) x^2+2x+1-y^2
3) x+y+z+x^2+xy+xz
4)xy+xz+y^2+yz
5)x^3+x^2+x+1
6)xy+y-2x-2
7)x^3+3x-3x^2-9
8)x^2+2xy+x+2y
9) x^2-y^2-2x-2y
10) 7x^2-7xy-5x=5y
a) 6x2 - 12x
= 6x(x - 2)
b) x2 + 2x + 1 - y2
= (x2 + 2x + 1) - y2
= (x + 1)2 - y2
= (x + 1 - y)(x + 1 + y)
c) x + y + z + x2 + xy + xz
= (x + x2) + (y + xy) + (z + xz)
= x(1 + x) + y(1 + x) + z(1 + x)
= (x + y + z)(x + 1)
d) xy + xz + y2 + yz
= (xy + xz) + (y2 + yz)
= x(y + z) + y(y + z)
= (x + y)(x + z)
e) x3 + x2 + x + 1
= (x3 + x2) + (x + 1)
= x2(x + 1) + (x + 1)
= (x2 + 1)(x + 1)
f) xy + y - 2x - 2
= (xy + y) - (2x + 2)
= y(x + 1) - 2(x + 1)
= (y - 2)(x + 1)
g) x3 + 3x - 3x2 - 9
= (x3 - 3x2) + (3x - 9)
= x2(x - 3) + 3(x - 3)
= (x2 + 3)(x - 3)
h) x2 - y2 - 2x - 2y
= (x2 - y2) - (2x + 2y)
= (x + y)(x - y) - 2(x + y)
= (x + y)(x - y - 2)
i) 7x2 - 7xy - 5x = 5y
mk thấy con này sai sai ý
i) 7x2 - 7xy - 5x + 5y
= (7x2 - 7xy) - (5x - 5y)
= 7x(x - y) - 5(x - y)
= (7x - 5)(x - y)
a) 3x(x+1)-x(3x+2)
b) 2x(x2-5x+6)+(x-1)(x+3)
c) (x2-xy+y2)-(x2+2xy+y2)
d) (2/5xy+x-y)-(3x+4y)-2/5xy
e) 2xy(x2-4xy+4y2)
f) (x+y)(xy+5)
g) (x3-2x2-x+2):(x-1)
h) (2x2+3x-2):(2x-1)
Tìm số nguyên x biết
a,3x+3y-2xy=7
b,xy+2x+y+11=0
c,xy+x-y=4
d,2x.(3y-2)+(3y-2)=12
e,3x+4y-xy=15
f,xy+3x-2y=11
g,xy+12=x+y
h,xy-2x-y=-6
i,xy+4x=25+5y
ii,2xy-6y+x=9
iii,xy-x+2y=3
k,2.x^2.y-x^2-2y-2=0
l,x^2.y-x+xy=6
