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1. -4x( x + 3 )( x - 4 ) - 3x( x2 - x + 1 )
= -4x( x2 - x - 12 ) - 3x( x2 - x + 1 )
= -4x3 + 4x2 + 48x - 3x3 + 3x2 - 3x
= -7x3 + 7x2 + 45x
2. a) 4x( x - 5 ) - ( x - 1 )( 4x - 3 ) = 5
<=> 4x2 - 20x - ( 4x2 - 7x + 3 ) = 5
<=> 4x2 - 20x - 4x2 + 7x - 3 = 5
<=> -13x - 3 = 5
<=> -13x = 8
<=> x = -8/13
b) 6( x - 3 )( x - 4 ) - 6x( x - 2 ) = 4
<=> 6( x2 - 7x + 12 ) - 6x2 + 12x = 4
<=> 6x2 - 42x + 72 - 6x2 + 12x = 4
<=> -30x + 72 = 4
<=> -30x = -68
<=> x = 34/15
Bài 1 :
\(-4x\left(x+3\right)\left(x-4\right)-3x\left(x^2-x+1\right)\)
\(=-7x^3+7x^2+45x\)
Bài 2 :
a, \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(\Leftrightarrow4x^2-20x-\left[4x^2-7x+3\right]=5\)
\(\Leftrightarrow4x^2-20x-4x^2+7x-3=5\)
\(\Leftrightarrow-13x-8=0\Leftrightarrow x=-\frac{8}{13}\)
b, \(6\left(x-3\right)\left(x-4\right)-6x\left(x-2\right)=4\)
\(\Leftrightarrow6x^2-42x+72-6x^2+12x=4\)
\(\Leftrightarrow-30x+68=0\Leftrightarrow x=\frac{34}{15}\)
a) ( x - 3 )( x + 3 )( x + 2 ) - ( x - 1 )( x2 - 3 ) - 5x( x + 4 )2 - ( x - 5 )2
= ( x2 - 32 )( x + 2 ) - ( x3 - x2 - 3x + 3 ) - 5x( x2 + 8x + 16 ) - ( x2 - 10x + 25 )
= x3 + 2x2 - 9x - 18 - x3 + x2 + 3x - 3 - 5x3 - 40x2 - 80x - x2 + 10x - 25
= ( x3 - x3 - 5x3 ) + ( 2x2 + x2 - 40x2 - x2 ) + ( -9x + 3x + 10x - 80x ) + ( -18 - 3 - 25 )
= -5x3 - 38x2 - 76x - 46
b) 2x( x - 4 )2 - ( x + 5 )( x - 2 )( x + 2 ) + 2( x + 5 )2 - ( x - 1 )2
= 2x( x2 - 8x + 16 ) - ( x + 5 )( x2 - 4 ) + 2( x2 + 10x + 25 ) - ( x2 - 2x + 1 )
= 2x3 - 16x2 + 32x - ( x3 + 5x2 - 4x - 20 ) + 2x2 + 20x + 50 - x2 + 2x - 1
= 2x3 - 16x2 + 32x - x3 - 5x2 + 4x + 20 + 2x2 + 20x + 50 - x2 + 2x - 1
= ( 2x3 - x3 ) + ( -16x2 - 5x2 + 2x2 - x2 ) + ( 32x + 4x + 20x + 2x ) + ( 20 + 50 - 1 )
= x3 - 20x2 + 58x + 69
c) ( x + 5 )2 - 4x( 2x + 3 )2 - ( 2x - 1 )( x + 3 )( x - 3 )
= x2 + 10x + 25 - 4x( 4x2 + 12x + 9 ) - ( 2x - 1 )( x2 - 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - ( 2x3 - x2 - 18x + 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - 2x3 + x2 + 18x - 9
= ( -16x3 - 2x3 ) + ( x2 - 48x2 + x2 ) + ( 10x - 36x + 18x ) + ( 25 - 9 )
= -18x3 - 46x2 - 8x + 16
d) -2x( 3x + 2 )( 3x - 2 ) + 5( x + 2 )2 - ( x - 1 )( 2x + 1 )( 2x - 1 )
= -2x( 9x2 - 4 ) + 5( x2 + 4x + 4 ) - ( x - 1 )( 4x2 - 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - ( 4x3 - 4x2 - x + 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - 4x3 + 4x2 + x - 1
= ( -18x3 - 4x3 ) + ( 5x2 + 4x2 ) + ( 8x + 20x + x ) + ( 20 - 1 )
= -22x3 + 9x2 + 29x + 19
Trả lời:
Bài 4:
b, B = ( x + 1 ) ( x7 - x6 + x5 - x4 + x3 - x2 + x - 1 )
= x8 - x7 + x6 - x5 + x4 - x3 + x2 - x + x7 - x6 + x5 - x4 + x3 - x2 + x - 1
= x8 - 1
Thay x = 2 vào biểu thức B, ta có:
28 - 1 = 255
c, C = ( x + 1 ) ( x6 - x5 + x4 - x3 + x2 - x + 1 )
= x7 - x6 + x5 - x4 + x3 - x2 + x + x6 - x5 + x4 - x3 + x2 - x + 1
= x7 + 1
Thay x = 2 vào biểu thức C, ta có:
27 + 1 = 129
d, D = 2x ( 10x2 - 5x - 2 ) - 5x ( 4x2 - 2x - 1 )
= 20x3 - 10x2 - 4x - 20x3 + 10x2 + 5x
= x
Thay x = - 5 vào biểu thức D, ta có:
D = - 5
Bài 5:
a, A = ( x3 - x2y + xy2 - y3 ) ( x + y )
= x4 + x3y - x3y - x2y2 + x2y2 + xy3 - xy3 - y4
= x4 - y4
Thay x = 2; y = - 1/2 vào biểu thức A, ta có:
A = 24 - ( - 1/2 )4 = 16 - 1/16 = 255/16
b, B = ( a - b ) ( a4 + a3b + a2b2 + ab3 + b4 )
= a5 + a4b + a3b2 + a2b3 + ab4 - ab4 - a3b2 - a2b3 - ab4 - b5
= a5 + a4b - ab4 - b5
Thay a = 3; b = - 2 vào biểu thức B, ta có:
B = 35 + 34.( - 2 ) - 3.( - 2 )4 - ( - 2 )5 = 243 - 162 - 48 + 32 = 65
c, ( x2 - 2xy + 2y2 ) ( x2 + y2 ) + 2x3y - 3x2y2 + 2xy3
= x4 + x2y2 - 2x3y - 2xy3 + 2x2y2 + 2y4 + 2x3y - 3x2y2 + 2xy3
= x4 + 2y4
Thay x = - 1/2; y = - 1/2 vào biểu thức trên, ta có:
( - 1/2 )4 + 2.( - 1/2 )4 = 1/16 + 2. 1/16 = 1/16 + 1/8 = 3/16
a) \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(\Leftrightarrow4x^2-20x-4x^2+7x-3=5\)
\(\Leftrightarrow-13x-3=5\)
\(\Leftrightarrow x=\frac{-8}{13}\)
b) \(\left(x-5\right)\left(x-1\right)=\left(x-1\right)\left(x-2\right)\)
\(\Leftrightarrow x^2-6x+5=x^2-3x+2\)
\(\Leftrightarrow-3x+3=0\)
\(\Leftrightarrow x=1\)
Vậy x=1
a )\(A=\frac{x^2+4x+4}{x^2-4}=\frac{\left(x+2\right)^2}{x^2-2^2}=\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}=\frac{x+2}{x-2}=\frac{5}{3}\)
<=> (x + 2).3 = (x - 2).5
<=> 3x + 6 = 5x - 10
<=> 3x - 5x = - 10 - 6
<=> - 2x = - 16
=> x = 8
b ) \(\frac{x+2}{x-2}=\frac{\left(x-2\right)+4}{x-2}=1+\frac{4}{x-2}\)
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