Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, Ta có :
\(N=x^2\left(y-1\right)-5x\left(1-y\right)=x^2\left(y-1\right)+5x\left(y-1\right)=x\left(x+5\right)\left(y-1\right)\)
Thay x = -20 ; y = 1001 ta được :
\(-20\left(-20+5\right)\left(1001-1\right)=-20.\left(-15\right).1000=300000\)
b, Ta có : \(x\left(x-y\right)^2-y\left(x-y\right)^2+xy^2-x^2y=\left(x-y\right)^3+xy\left(x-y\right)\)
\(=\left(x-y\right)^4\left(1+xy\right)\)
Thay x - y = 7 ; xy = 9 ta được :
\(7^4.\left(1+9\right)=2401.10=24010\)
N = x2( y - 1 ) - 5x( 1 - y )
= x2( y - 1 ) + 5x( y - 1 )
= x( y - 1 )( x + 5 )
Tại x = -20 ; y = 1001 ta được :
N = -20( 1001 - 1 )( -20 + 5 )
= -20.1000.(-15)
= 1000.300
= 300 000
Q = x( x - y )2 - y( x - y )2 + xy2 - x2y
= x( x - y )2 - y( x - y )2 - xy( x - y )
= ( x - y )[ x( x - y ) - y( x - y ) - xy ]
= ( x - y )( x2 - xy - xy + y2 - xy )
= ( x - y )( x2 - 3xy + y2 )
= ( x - y )[ ( x2 - 2xy + y2 ) + 2xy - 3xy ]
= ( x - y )[ ( x - y )2 - xy ]
= 7[ 72 - 9 ]
= 7( 49 - 9 )
= 7.40 = 280
a: \(x-2-\frac{x^2-10}{x+2}\)
\(=\frac{\left(x-2\right)\left(x+2\right)-x^2+10}{x+2}\)
\(=\frac{x^2-4-x^2+10}{x+2}=\frac{6}{x+2}\)
b: \(\frac{x}{y^2-xy}-\frac{y}{xy-x^2}\)
\(=\frac{-x}{y\left(x-y\right)}+\frac{y}{x\left(x-y\right)}=\frac{-x^2+y^2}{xy\left(x-y\right)}=\frac{-\left(x-y\right)\left(x+y\right)}{xy\left(x-y\right)}\)
\(=\frac{-x-y}{xy}\)
c: \(\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}\)
\(=-\frac{1}{x}+\frac{1}{x-1}-\frac{1}{x-1}+\frac{1}{x-2}-\frac{1}{x-2}+\frac{1}{x-3}-\frac{1}{x-3}+\frac{1}{x-4}-\frac{1}{x-4}+\frac{1}{x-5}\)
\(=\frac{1}{x-5}-\frac{1}{x}=\frac{x-\left(x-5\right)}{x\left(x-5\right)}=\frac{5}{x\left(x-5\right)}\)