Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3\\ =6x^2y+2y^3=2y\left(3x^2+y^2\right)\)Vậy \(\left(x+y\right)^3-\left(x-y\right)^3=2y\left(3x^2+y^2\right)\)
1)rút gọn
a) (x+5)(\(x^2\) - 5x + 25) - \(\left(x+3\right)^3\) + (x-2)(\(x^2\) + 2x + 4) - \(\left(x-1\right)^3\)
b)\(\left(x+3y\right)^3+\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)-\left(2y-3x\right)^3\)
c)\(\left(3x+y\right)^3-\left(5x-y\right)\left(25x^2+5xy+y^2\right)+\left(x+2y\right)^3\)
2)tìm x,biết
a)\(\left(x-1\right)^2-\left(x-2\right)\left(x+3\right)+\left(x+2\right)^3=\left(x-3\right)\left(x^2+3x+9\right)+6x\left(x+2\right)\)
Cảm ơn các bạn ^^
chứng minh \(\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2=\left(y+z-2x\right)^2+\left(z+x-2y\right)^2+\left(y+z-2z\right)^2\)
thì x=y=z
b) \(\left(a+b+c+d\right)\left(a-b+c-d\right)=\left(a^2-b+c-d\right)\left(a+b-c-d\right)\)
thì ad=bc
Chứng minh không tồn tại x,y,z thỏa mãn
a) \(5x^2+10y^2-6xy-4x-2y+3\)=0
b) \(x^2+4y^2+z^2-2x-6x+6y+15=0\)
1>Tínk:
1, \(\left(x+y\right)^3-\left(x-y\right)^3\)
2, 64-24y+\(3y^2-\dfrac{1}{8}y^3\)
3, \(216x^3+18x^2y+\dfrac{1}{2}xy^2+\dfrac{1}{216}y^3\)
4, \(\left(2x+y\right)^3-3.\left(x+y\right).\left(x-y\right)\)
5, \(\left(x-y\right)^3+3.\left(x+y\right).\left(x^2+y^2\right)\)
Rút gọn các biểu thức sau :
a) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
b) \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
Rút gọn các biểu thức sau:
a, \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
b, \(\left(2x+y\right).\left(4x^2-2xy+y^2\right)-\left(2x-y\right).\left(4x^2+2xy+y^2\right)\)
Bài 1.Tính
a) \(\left(x+4\right)^3\)
b) \( \left(2x-5\right)^3\)
c) \(\left(\dfrac{1}{2}-x\right)^3\)
d) \(\left(-3x-2y\right)^3\)
e)\(\left(2x^2y-3xy^2\right)^3\)
f)\(\left(x+\dfrac{1}{3}y^2\right)^3\)
rút gọn
\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)+\left(3x-y\right)\left(9x^2+3xy+y^2\right)-35\left(x-1\right)\left(x^2+x+1\right)\)
Tính :
a) \(\left(2+xy\right)^2\)
b) \(\left(5-3x\right)^2\)
c) \(\left(5-x^2\right)\left(5+x^2\right)\)
d) \(\left(5x-1\right)^3\)
e) \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
f) \(\left(x+3\right)\left(x^2-3x+9\right)\)
cho x+y=5, tính giá trị biểu thức:
Q=\(^{x^3+y^3-2x^2-2y^2+3xy\times\left(x+y\right)-4xy+3\times\left(x+y\right)}\)