2x . (3y-2) +(3y-2)=-55
tìm x,y
Rút gọn mỗi biểu thức sau:
a, (2x-1)\(^2\)-(x-3).(x+3)-1969
b, (2x-3y).(2x+3y)-(2x-y)\(^2\)
c, (x+3y)\(^2\)+(x-y).(x+y)+280
\(a,\left(2x-1\right)^2-\left(x-3\right)\left(x+3\right)-1969\\ =4x^2-4x+1-x^2+9-1969\\ =3x^2-4x-1959\)
\(b,\left(2x-3y\right)\left(2x+3y\right)-\left(2x-y\right)^2\\ =4x^2-9y^2-4x^2+4xy-y^2\\ =8y^2+4xy=4y\left(2y+x\right)\)
\(c,\left(x+3y\right)^2+\left(x+y\right)\left(x-y\right)+280\\ =x^2+6xy+9y^2+x^2-y^2+280\\ =2x^2+8y^2+6xy+280\)
a: \(\left(2x-1\right)^2-\left(x-3\right)\cdot\left(x+3\right)-1969\)
\(=4x^2-4x+1-x^2+9-1969\)
\(=3x^2-4x-1959\)
b: \(\left(2x-3y\right)\left(2x+3y\right)-\left(2x-y\right)^2\)
\(=4x^2-9y^2-4x^2+4xy-y^2\)
\(=-10y^2+4xy\)
a)\(\text{( 2 x − 1 )^2− ( x − 3 ) ( x + 3 ) − 1969}\)
\(\text{= 4x^2 − 4x + 1 − x^2 + 9 − 1969}\)
\(\text{=3x^2− 4 x − 1959}\)
b) \(\text{( 2 x − 3 y ) ( 2 x + 3 y ) − ( 2 x − y )^2}\)
=\(\text{= 4 x^2− 9 y^2− 4 x^2 + 4 x y − y^2}\)
\(\text{= -10 y^2+ 4 x y = -2 y ( 5 y -2 x )}\)
c)\(\text{( x + 3 y )^2 + ( x + y ) ( x − y ) + 280}\)
\(\text{= x^2 + 6 x y + 9 y^2 + x^2 − y^2 + 280}\)
\(\text{= 2 x^2 + 8 y^2 + 6 x y + 280}\)
x-y=x+z=y-z= x-2
2x-3y=2x+3y;3y-2z=3y+2z và x-2y+2=3
x/2=y/-3=2/4 và x-y+3=z
(2x+3y)(2x-3y)-(2x-1)^2+(3y-1)^2 với x=1;y=-1
\(\left(2x+3y\right)\left(2x-3y\right)-\left(2x-1\right)^2+\left(3y-1\right)^2\)
\(=4x^2-9y^2-4x^2+4x-1+9y^2-6y+1=4x-6y\)
Thay x = 1 ; y = -1 ta được :
\(4+6=10\)
Bất phương trình nào sau đây là bất phương trình bậc nhất hai ẩn?
a) \(2x^2+3y>0\)
b) 2x + \(3y^2\le0\)
c) 2x + 3y > 0
d) \(2x^2-y^2+3x-2y< 0\)
e) 3y < 1
f) x - 2y \(\le1\)
g) x \(\le0\)
h) y > 0
i) 4(x-1) + 5(y-3) > 2x - 9
Bất phương trình bậc nhất 2 ẩn :
\(2x+3y>0\Rightarrow Câu\) \(C\)
\(x-2y\le1\Rightarrow Câu\) \(f\)
\(4\left(x-1\right)+5\left(y-3\right)>2x-9\)
\(\Leftrightarrow4x-4+5y-15-2x+9>0\)
\(\Leftrightarrow2x+5y-10>0\) \(\Rightarrow Câu\) \(i\)
\(tính M= { 2x-3y/2x+3y} với x^2-2xy=3y^2 x+y khác 0, y khác 0 2x+3 khác 0\)
37. Phân tích đa thưc 2x^3y - 2xy^3 - 4xy^2 - 2xy thành nhân tử ta đc:
A. 2xy (x-y-1) (x+y-1)
B. 16x - 54y^3 = 2(2x-3y) (4x^2 + 6xy + 9y^2)
C. 16x^3 - 54y = 2(2x - 3y) (2x + 3y) ^2
D. 16x^4 (x-y) - x + y = (4x^2 -1) (4x^2 + 1) (x-y)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy.\left(x^2-y^2-2y-1\right)\)
\(=2xy.[x^2-\left(y^2+2y+1\right)]\)
\(=2xy.[x^2-\left(y+1\right)^2]\)
\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)
Vậy chọn đáp án A
Rút gọn biểu thức:
a) 2x(x-3y)+3y(2x + 5y)
b) (5x-3y)(2x+y)-x(10x-y)
c) (x-y)(x2+xy+y2)-(x+y)(x2-xy+y2)
a) 2x(x-3y)+3y(2x+5y)
=2x2-6xy+6xy+15y2
=2x2+15y2
b)(5x-3y)(2x+y)-x(10x-y)
=10x2+5xy-6xy-3y2-10x2+xy
=0
c)(x-y)(x2+xy+y2)-(x+y)(x2-xy+y2)
=x3-y3-(x3+y3)
=x3-y3-x3-y3
=-2y3
Tính nhanh
a,(2x-3)2
b,(x-3y)2
c, (2x+3y) (2x-3y)-(2x+y)2
d,(x+3y2)2
a: \(\left(2x-3\right)^2=4x^2-12x+9\)
b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)
c: \(=4x^2-9y^2-4x^2-4xy-y^2\)
\(=-10y^2-4xy\)
d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)
Tính nhanh
a,(2x-3)2
b,(x-3y)2
c, (2x+3y) (2x-3y)-(2x+y)2
d,(x+3y2)2
a: \(\left(2x-3\right)^2=4x^2-12x+9\)
b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)
c: \(\left(2x+3y\right)\left(2x-3y\right)-\left(2x+y\right)^2\)
\(=4x^2-9y^2-4x^2-4xy-y^2=-8y^2-4xy\)
d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)
Rút gọn biểu thức:
a) (x+y)^2+(x-y)^2+(x+y).(x-y)
b) (3x+y)^2+(x-3y)2-(2x+y).(2x-y)
c) 2(x-y).(x+y)+(x+y)^2+(x-y)^2
d)-2(x^2-9y^2)+(x-3y)^2+(x+3y)^2
a) \(\left(x+y\right)^2+\left(x-y\right)^2+\left(x+y\right)\left(x-y\right)\)
\(=x^2+2xy+y^2+x^2-2xy+y^2+x^2-y^2\)
\(=3x^2+y^2\)
b)\(\left(3x+y\right)^2+\left(3x-y\right)^2-\left(2x+y\right)\left(2x-y\right)\)
\(=9x^2+6xy+y^2+9x^2-6xy+y^2-4x^2+y^2\)
\(=14x^2+3y^2\)
c) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
\(=\left(x-y\right)^2+2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x-y+x+y\right)^2\)
\(=4x^2\)
d)\(-2\left(x^2-9y^2\right)+\left(x-3y\right)^2+\left(x+3y\right)^2\)
\(=\left(x+3y\right)^2-2\left(x+3y\right)\left(x-3y\right)+\left(x-3y\right)^2\)
\(=\left(x+3y-x+3y\right)^2=9y^2\)