y=2x-3 / x+2
Rút gọn:
a)2x.(3x-1)-(x-3).(6x+2)
b)(2x-3)2-(1+2x).(2x-1)+3.(2x-3)
c)(x+y-1)2-2.(x+y-1).(x+y)+(x+y)2
a: Ta có: \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)\)
\(=6x^2-2x-6x^2-2x+18x+6\)
=14x+6
b: Ta có: \(\left(2x-3\right)^2-\left(2x+1\right)\left(2x-1\right)+3\left(2x-3\right)\)
\(=4x^2-12x+9-4x^2+1+6x-9\)
\(=-6x+1\)
c: Ta có: \(\left(x+y-1\right)^2-2\left(x+y-1\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x+y-1-x-y\right)^2\)
=1
a) \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)=6x^2-2x-6x^2-2x+18x+6=14x+6\)
b) \(\left(2x-3\right)^2-\left(1+2x\right)\left(2x-1\right)+3\left(2x-3\right)=4x^2-12x+9-4x^2+1+6x-9=-6x+1\)
c) \(\left(x+y-1\right)^2-2\left(x+y-1\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-1-x-y\right)^2=\left(-1\right)^2=1\)
Bài 3: Rút gọn biểu thức (Dùng hằng đẳng thức)
1, (x+y)\(^2\)-(x-y)\(^2\)
2, (x+y)\(^3\)-(x-y)\(^3\)-2y\(^3\)
3,(x+y)\(^2\)-2(x+y)(x-y)+(x-y)\(^2\)
4,(2x+3)\(^2\)-2(2x+3)(2x+5)+(2x+5)\(^2\)
5, 9\(^8\). 2\(^8\)-(18\(^4\)+1)(18\(^4\)-1)
\(1,\left(x+y\right)^2-\left(x-y\right)^2=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)+\left(x-y\right)\right]=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)
\(2,\left(x+y\right)^3-\left(x-y\right)^3-2y^3\)
\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3\)
\(=6x^2y\)
\(3,\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =4y^2\)
\(4,\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\\ =\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\\ =\left(2x+3-2x-5\right)^2\\ =\left(-2\right)^2\\ =4\)
\(5,9^8.2^8-\left(18^4+1\right)\left(18^4-1\right)\\ =18^8-\left[\left(18^4\right)^2-1\right]\\ =18^8-18^8+1\\ =1\)
1: =x^2+2xy+y^2-x^2+2xy-y^2=4xy
2: =x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3
=6x^2y
3: =(x+y-x+y)^2=(2y)^2=4y^2
4: =(2x+3-2x-5)^2=(-2)^2=4
5: =18^8-18^8+1=1
*Cộng các phân thức sau: a) x^2/x+1 + 2x/x^2-1 + 1/1+x+1 b) 2x+y/2x^2-y + 8y/y^2-4x^2+2x-y/2x^2+xy c) 1/x-y +3xy/y^3-x^3 + x-y/x^2+xy+y^2
a, \(\frac{x^2}{x+1}+\frac{2x}{x^2-1}+\frac{1}{x+1}+1\)
\(=\frac{x^2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}-\frac{2x}{\left(x-1\right)\left(x+1\right)}+\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x^3-x^2-2x+x-1-x^2-1}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^3-2x^2-x-2}{\left(x-1\right)\left(x+1\right)}\)
tính
a) x. (2x2 - 3) - x2 (5x +1 ) -x2
b) 2(x-2) . (x+3) + (x - 2)2 + (x + 3)2
c) ( 2x +y) 3. (2x - y )2
d) ( 2x - 3 ) . (2x+3) - (x+5)2 - (x-1) . (x+2)
a: =2x^3-3x-5x^3-x^2-x^2
=-3x^3-2x^2-3x
b: =2(x^2+x-6)+x^2-4x+4+x^2+6x+9
=2x^2+2x-12+2x^2+2x+13
=4x^2+4x+1
d: =4x^2-9-x^2-10x-25-x^2-x+2
=2x^2-11x-32
làm phép chia
4x^2(y+z)^5:2x(y+z)^3
-x^2(y-1)^3(z+2)^2:1/2x^2(y-1)^2
x^m+1(y+2)^m:y(y+2)
3/4(x+2)^2m(x-3)^n-2:2/3(x+2)(x-3)^2
\(\dfrac{4x^2\left(y+z\right)^5}{2x\left(y+z\right)^3}=2x\left(y+z\right)^2\)
phân tích thành nhân tử
x^3+2x^2+x-xy
x^3-y^3+2x^2-2y^2
x^3+y^3+x^2y+y^2x+2^2x+2^2y
a, \(x^3+2x^2+x-xy=x\left(x^2+2x+1-y\right)\)
\(=x\left[\left(x+1\right)^2-y\right]\)
b, \(x^3-y^3+2x^2-2y^2=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left[\left(x^2+xy+y^2\right)+2\left(x+y\right)\right]\)
\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)
Bài 1 làm tính nhân
2x.(x^2-7x-3)
(-2x^3+y^2-7xy).4xy^2
(-5x^3).(2x^2+3x-5)
(2x^2-xy+y^2).(-3x^3)
(x^2-2x+3).(x-4)
(2x^3-3x-1).(5x+2)
Bài 2 Thực hiện phép tính
A,(2x+3y^2)
B, (5x-y)^2
C, (2x+y^2)^3
D, ( 3x^2-2y)^3
\(2x\left(x^2-7x-3\right)=2x^3-14x-6x\)
\(4xy^2\left(-2x^3+y^2-7xy\right)=-8x^4y^2+4xy^5-28x^2y^3\)
Cho x-y-2 = 0 . Tính
A= x3 + x2y - 2x2 - xy - y2 + 3y + x -1
B = x3 + x2y - 2x2 - x2y - xy2 + 2xy + 2y +2x - 2
C = x4 + 2x3y - 2x3 + x2y2 - 2x2y - x(x+y) + 2x + 3
8x^3(y+z)-y^3(z+2x)-2x^3(2x-y)
(x^2+y^2)^3+(z^2-x^2)^3-(y^2+z^2)^3