rút gọn biểu thức sau
(2x-y+z)+(y-z+x)+(z-2x+y)Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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2x + y + 3z - ( x - y + z )
= 2x + y + 3z - x + y - z
= x + 2y + 2z
\(\left(2x+y+3z\right)-\left(x-y+z\right)\)
\(=2x+y+3z-x+y-z\)
\(=x+2y+2z\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b: \(B=\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)
\(=\dfrac{\left(x+y-z\right)\left(x+y+z\right)}{x+y+z}\)
=x+y-z
c:
ĐKXĐ: x<>1
\(C=\dfrac{x^2-6x+5}{x^2-2x+1}\)
\(=\dfrac{\left(x-1\right)\left(x-5\right)}{\left(x-1\right)^2}\)
\(=\dfrac{x-5}{x-1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\dfrac{2x^2-2xy}{x^2+x-xy-y}\) \(\left(x\ne y;x\ne-1\right)\)
\(=\dfrac{2x\left(x-y\right)}{x\left(x+1\right)-y\left(x+1\right)}\)
\(=\dfrac{2x\left(x-y\right)}{\left(x-y\right)\left(x+1\right)}\)
\(=\dfrac{2x}{x+1}\)
b) \(\dfrac{x^2+y^2-z^2+2xy}{x^2-y^2+z^2+2xz}\)
\(=\dfrac{\left(x^2+2xy+y^2\right)-z^2}{\left(x^2+2xz+z^2\right)-y^2}\)
\(=\dfrac{\left(x+y\right)^2-z^2}{\left(x+z\right)^2-y^2}\)
\(=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{\left(x-y+z\right)\left(x+y+z\right)}\)
\(=\dfrac{x+y-z}{x-y+z}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
- a,(2+xy)^2=4+4xy+x^2y^2
- b,(5-3x)^2=25-30x+9x^2
- d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1
![](https://rs.olm.vn/images/avt/0.png?1311)
Trog những HĐT trên chắc là
bn đánh máy thiếu số mũ nhỉ??
Phải ko
1.\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=\left(2x\right)^3+y^3-\left(2x\right)^3+y^3=2y^3\)
2. \(2\left(2x+1\right)\left(3x-1\right)+\left(2x+1\right)^2+\left(3x-1\right)^2\)
\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)
3. \(\left(x-y+z\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z+y-z\right)^2=x^2\)
4. \(\left(x-3\right)\left(x+3\right)-\left(x-3\right)^2\)
\(=\left(x-3\right)\left(x+3-x+3\right)=6\left(x-3\right)\)
5. \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3+2x^2-x-2-x^3+y^3=2x^2-x-2+y^3\)
6. Áp dụng các hằng đẳng thức đáng nhớ
![](https://rs.olm.vn/images/avt/0.png?1311)
Trả lời:
g) G = ( 3x + 5 ).( 2x - 1 ) + ( 4x - 1 ).( 3x + 2 )
= 6x2 - 3x + 10x - 5 + 12x2 + 8x - 3x - 2
= 18x2 + 12x - 7
Ta có: | x | = 2 => x = 2 hoặc x = - 2
Thay x = 2 vào G, ta có:
G = 18.22 + 12.2. - 7 = 89
Thay x = - 2 vào G, ta có:
G = 18.(- 2 )2 + 12.( - 2 ) - 7 = 41
h) H = ( 2x + y ).( 2z + y ) + ( x - y ).( y - z )
= 4xz + 2xy + 2yz + y2 + xy - xz - y2 + yz
= 3xz + 3xy + 3yz
Ta có: z = | 1 | = 1
Thay x = 1; y = 1; z = 1 vào H, ta có:
H = 3.1.1 + 3.1.1 + 3.1.1 = 9
(2x-y+z)+(y-z+x)+(z-2x+y)
= 2x - y + z + y - z + x + z - 2x + y
= (2x - 2x + x) + (y - y + y) + ( z - z + z)
= x + y + z
Cảm ơn bạn nhiều