Chứng minh :
a) \(\left(x-1\right)\left(x^2+x+1\right)=x^3-1\)
b) \(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4-y^4\)
1.tìm x
a) \(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)\)
b) \(4\left(x-1\right)\left(x+5\right)-\left(x+2\right)\left(x+5\right)=3\left(x-1\right)\left(x+2\right)\)
2. CMR
a) \(\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)=x^5-y^5\)
b)\(\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)=x^5+y^5\)
c)\(\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab\)
giúp mik nha
chiều nay nộp r
Chứng minh:
a. \(X^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
b.\(S=a+b+c\) thì
\(S\left(S-2b\right)\left(S-2c\right)+S\left(S-2c\right)\left(S-2a\right)+S\left(S-2a\right)\left(S-2b\right)=\left(S-2a\right)\left(S-2b\left(S-2c\right)+8abc\right)\)
Làm tính nhân :
a) \(\left(x^2y^2-\dfrac{1}{2}xy+2y\right)\left(x-2y\right)\)
b) \(\left(x^2-xy+y^2\right)\left(x+y\right)\)
Thực hiện phép tính :
a) \(\left(5x-2y\right)\left(x^2-xy+1\right)\)
b) \(\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
c) \(\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)\)
Thực hiện các phép tính sau:
a).\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b). \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c). \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
d). \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Cho x>0;y>0;x+y=2018
a)tìm GTLN của B=\(\dfrac{2x^2+8xy+2y^2}{x^2+2xy+y^2}\)
b)TÌm GTNN của C=\(\left(1+\dfrac{2012}{x}\right)^2+\left(1+\dfrac{2012}{y}\right)^2\)
Chứng tỏ biểu thức sau không phụ thuộc vào biến x,y:
\(\left(x-1\right)\left(x^2+y\right)-\left(x^2-y\right)\left(x-2\right)-x\left(x+2y\right)+3\left(y-5\right)\)Rút gọn biểu thức :
a) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-2\right)\)
b) \(\left(4x^2-3y\right).2y-\left(3x^2-4y\right).3y\)
c) \(3y^2\left[\left(2y-1\right)+y+1\right]-y\left(1-y-y^2\right)+y\)
mình cần gấp ạ bạn naok tl nhanh mình tick luôn nhé
