Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(a,\left(x+2\right)^2-\left(x-2\right)^2-2\left(x-2\right)\left(x+2\right).\)
\(=\left(x+2-x+2\right)^2=4^2=16\)
\(b,\left(x-y\right)^2+\left(x+y\right)^2+2\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y+x+y\right)^2=x^2\)
\(c,\left(x-y+z\right)^2-2\left(x+y\right)-2\left(x+y\right)\left(x-y\right)-z^2\)
A=\(\frac{x^2}{\left(x+y\right)\left(1-y\right)}-\frac{y^2}{\left(x+y\right)\left(1+x\right)}\)\(-\frac{x^2y^2}{\left(1+x\right)\left(1-y\right)}\)
A=\(\frac{x^2\left(1+x\right)-y^2\left(1-y\right)-x^2y^2\left(x+y\right)}{\left(1+x\right)\left(1-y\right)\left(x+y\right)}\)
A=\(\frac{x^2+x^3-y^2+y^3-x^2y^2\left(x+y\right)}{\left(1+x\right)\left(1-y\right)\left(x+y\right)}\)
A=\(\frac{\left(x+y\right)\left(x-y\right)+\left(x+y\right)\left(x^2-xy+y^2\right)-x^2y^2\left(x+y\right)}{\left(1+x\right)\left(1+y\right)\left(x+y\right)}\)
A=\(\frac{\left(x+y\right)\left(x-y+x^2-xy+y^2-x^2y^2\right)}{\left(x+y\right)\left(x+1\right)\left(1-y\right)}\)
A=\(\frac{x\left(x+1\right)-y\left(x+1\right)+y^2\left(1-x\right)\left(1+x\right)}{\left(x+1\right)\left(1-y\right)}\)
A=\(\frac{\left(x+1\right)\left(x-y+y^2-y^2x\right)}{\left(x+1\right)\left(1-y\right)}\)
A=\(\frac{-y\left(1-y\right)+x\left(1-y\right)\left(1+y\right)}{\left(1-y\right)}\)
A=\(\frac{\left(1-y\right)\left(-y+x+xy\right)}{1-y}\)=\(x-y+xy\)
\(A=\left(x-y\right)^2-2\left(x^2-xy-y^2\right)=x^2-2xy+y^2-2x^2+2xy+2y^2\)
\(=-x^2+3y^2\)
\(a,\left(x-2\right)^3-x\left(x-1\right)\left(x+1\right)+6x\left(x-3\right)\)
\(=x^3-6x^2+12x-27-x^3+x+6x^2-18x\)
\(=-5x-27\)
\(b,\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-\left(8x^3-y^3\right)\)
\(=8x^3+y^3-8x^3+y^3=2y^3\)
\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x+y+z-x-y\right)^2\)
\(=z^2\)
a)
=\(x^3-6x^2+12x+8-27-x^3+x+6x^2-18x\)
=-5x-19
b)
=\(8x^3+y^3-8x^3+y^3\)
=\(2y^3\)
c)
=(x+y+z-x-y)\(^2\) +x+y
=\(z^2+x+y\)
hc tốt
\(3\left(x-y\right)^2-2\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)\)
\(=3.\left(x^2-2xy+y^2\right)-2\left(x^2+2xy+y^2\right)-x^2+y^2\)
\(=3x^2-6xy+3y^2-2x^2-4xy-2y^2-x^2+y^2\)
\(=2y^2-10xy\)
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)\(-2\left(x^2-9y^2\right)+\left(x-3y\right)^2+\left(x+3y\right)^2\)
\(=\left(x+3y\right)^2-2\left(x+3y\right)\left(x-3y\right)+\left(x-3y\right)^2\)
\(=\left(x+3y-x+3y\right)^2=9y^2\)
( x + y )2 + ( x - y )2
= ( x + y ) . ( x + y ) + ( x - y ) . ( x - y )
= ( x2 + xy ) + ( xy + y2 ) + ( x2 - xy ) - ( xy - y2 )
= x2 + xy + xy + y2 + x2 - xy - xy - y2
= ( x2 + x2 ) + ( xy + xy ) + ( y2 - y2 ) + ( -xy - xy )
= 2x2 + 2xy - 2xy
= 2x2
a. \(x\left(x+y\right)+y\left(x-y\right)=x^2+xy+xy-y^2=x^2+2xy-y^2\)
b. \(x\left(x^2-y\right)+x\left(y^2-y\right)-x\left(x^2+y^2\right)=x^3-xy+xy^2-xy-x^3-xy^2=-2xy\)