Rút gọn:
a, 5(2x-1)-2(5x+3)
b, 3(x+y)-3(x-2xy+y)
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a: Ta có: \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)\)
\(=6x^2-2x-6x^2-2x+18x+6\)
=14x+6
b: Ta có: \(\left(2x-3\right)^2-\left(2x+1\right)\left(2x-1\right)+3\left(2x-3\right)\)
\(=4x^2-12x+9-4x^2+1+6x-9\)
\(=-6x+1\)
c: Ta có: \(\left(x+y-1\right)^2-2\left(x+y-1\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x+y-1-x-y\right)^2\)
=1
a) \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)=6x^2-2x-6x^2-2x+18x+6=14x+6\)
b) \(\left(2x-3\right)^2-\left(1+2x\right)\left(2x-1\right)+3\left(2x-3\right)=4x^2-12x+9-4x^2+1+6x-9=-6x+1\)
c) \(\left(x+y-1\right)^2-2\left(x+y-1\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-1-x-y\right)^2=\left(-1\right)^2=1\)
a: \(x^4y-5x^4y-5xy^3+2xy^3=-4x^4y-3xy^3\)
b: \(5xy^4-5xy+7xy-2xy^4=3xy^4+2xy\)
Bài 1:
A = 5x(x - y) - y(5x - y)
A = 5x2 - 5xy - 5xy + y2
A = 5x2 - 10xy + y2 (1)
Thay x = -1; y = 3 vào (1), ta có:
5.(-1)2 - 10.(-1).3 + 32 = 44
B = 4y(x2 - 3xy + 3y2) - 2xy(2x - 6y - 3)
B = 4x2y - 12x2 + 12y3 - 4x2y + 12xy2 + 6xy
B = 12y3 + 6xy (1)
Thay x = 5; y = -1 vào (1), ta có:
12.(-1)3 + 6.5.(-1) = -42
C = 5x2(x - y2) + 3x(xy2 - y) - 5x3
C = 5x3 - 5x2y2 + 3x2y2 - 3xy - 5x3
C = -2x2y2 - 3xy (1)
Thay x = -2; y = -5 vào (1), ta có:
-2.(-2)2.(-5)2 - 3.(-2).(-5) = -230
D = 6x2(y2 - xy + 2x2y) - 3xy(2xy - x2 + 4x3)
D = 6x2y2 - 6x3y + 12x4y - 6x2y2 + 3x3y - 12x4y
D = -3x3y (1)
Thay x = 11; y = -1 vào (1), ta có:
-3.113.(-1) = 3993
a) `(2x+5)^3-(2x-5)^3-(120x^2+49)`
`=(2x+5-2x+5)[(2x+5)^2+(2x+5)(2x-5)+(2x-5)^2]-(120x^2+49)`
`=10(12x^2+25)-(120x^2+49)`
`=120x^2+250-120x^2-49`
`=201`
b) `(4-5x)^2-(3+5x)^2=(4-5x+3+5x)(4-5x-3-5x)=7.(-10x+1)=-70x+7`
Lời giải:
a.
$(2x+5)^3-(2x-5)^3-(120x^2+49)$
$=[(2x+5)-(2x-5)][(2x+5)^2+(2x+5)(2x-5)+(2x-5)^2]-(120x^2+49)$
$=10(4x^2+20x+25+4x^2-25+4x^2-20x+25)-(120x^2+49)$
$=10(12x^2+25)-(120x^2+49)=250-49=201$
b.
$(4-5x)^2-(3+5x)^2=[(4-5x)+(3+5x)][(4-5x)-(3+5x)]$
$=7(1-10x)$
a: Khi x>0 thì A=3x-3x+2=2
Khi x<0 thì A=-3x-3x+2=-6x+2
b: B=4-x-x+5=9-2x
c: TH1: 5/4<x<5/2
A=5-2x-3x+7=12-5x
TH2: x>=5/2
A=2x-5-3x+7=-x+2
d: D=3-5x+|5x-3|
TH1: x>=3/5
D=3-5x+5x-3=0
TH2: x<3/5
D=3-5x+3-5x=6-10x
a) ( x + 2 )( x2 - 2x + 4 ) - ( 18 + x3 )
= x3 + 8 - 18 - x3 = -10
b) ( 2x - y )( 4x2 + 2xy + y2 ) - ( 2x + y )( 4x2 - 2xy + y2 )
= 8x3 - y3 - ( 8x3 + y3 )
= 8x3 - y3 - 8x3 - y3 = -2y3
c) ( x - 3 )( x + 3 ) - ( x + 5 )( x - 1 )
= x2 - 9 - ( x2 + 4x - 5 )
= x2 - 9 - x2 - 4x + 5 = -4x - 4
d) ( 3x - 2 )2 + ( x + 1 )2 + 2( 3x - 2 )( x + 1 )
= ( 3x - 2 + x + 1 )2
= ( 4x - 1 )2
a, \(5\left(2x-1\right)-2\left(5x+3\right)=10x-5-10x-6=-11\)
b, \(3\left(x+y\right)-3\left(x-2xy+y\right)\)
\(=3\left[\left(x+y\right)-\left(x-2xy+y\right)\right]=3\left(x+y-x+2xy-y\right)\)
\(=3.2xy=6xy\)