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a, \(\left(x+2\right)\left(2-x\right)-\left(2x-1\right)\left(x+3\right)\)
\(=4-x^2-\left(2x^2+5x-3\right)=4-x^2-2x^2-5x+3=-3x^2-5x+7\)
b, \(\left(x+1\right)^2-2\left(x^2-1\right)+\left(x-1\right)^2=\left(x+1\right)^2-2\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\)
\(=\left(x+1-x+1\right)^2=2^2=4\)
c, \(\left(x+y\right)^3-\left(x-y\right)^2-6x^2y\)
\(=x^3+3x^2y+3xy^2+y^3-x^2+2xy-y^2-6x^2y\)
\(=x^3-3x^2y+3xy^2+y^3-x^2+2xy-y^2\)
a)B=3x3 -2y3-6x2y2+xy
B=(3x3-6x2y2)+(xy-2y3)
B=3x2(x-2y2)+y(x-2y2)
B=(x-2y2)(3x2+y)
tại x=\(\frac{2}{3}\)và y=\(\frac{1}{2}\)ta có B=(x-2y2)(3x2+y)=(\(\frac{2}{3}\)-2*\(\frac{1}{2}\)^2 )(3*\(\frac{2}{3}\)^2+\(\frac{1}{2}\))=\(\frac{1}{6}\)*\(\frac{11}{6}\)=\(\frac{11}{36}\)
b)C= 2x+xy2-x2y-2y
C=(2x-2y)+(xy2-x2y)
C=2(x-y)-xy(x-y)
C=(2-xy)(x-y)
tại x=\(-\frac{1}{2}\)và y=\(-\frac{1}{3}\)ta có C=(2-xy)(x-y)=(2-\(-\frac{1}{2}\)*\(-\frac{1}{3}\))(\(-\frac{1}{2}\)+\(\frac{1}{3}\))=\(\frac{-11}{36}\)
a: =18x^3y^2-12x^3y^3+6x^2y^2
b: (-3x+2)(5x^2-1/3x+4)
=-12x^3+x^2-12x+10x^2-2/3x+8
=-12x^3+11x^2-38/3x+8
c: =x^2-x-2+3x-x^2
=2x-2
d: =4x^2+12x+9-4x^2+25-(x-1)(x^2+12)
=12x+34-x^3-12x+x^2+12
=-x^3+x^2+46
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
+) \(A=x^2-y+xy^2-x\)
\(A=\left(x^2-y\right)+\left(xy^2-x\right)\)
\(A=\left(x^2-y\right)+x\left(y^2-1\right)\)
Tại x = -5, y = 2 ta có :
\(A=\left[\left(-5\right)^2-2\right]+\left(-5\right)\left(2^2-1\right)=8\)
+) \(B=3x^3-2y^3-6x^2y^2\)
\(B=3x^3-\left(2y^3+6x^2y^2\right)=3x^3-2y^2\left(y+3x^2\right)\)
Tại x = 2/3, y = 1/2 ta có :
\(B=3.\left(\dfrac{2}{3}\right)^3-2.\left(\dfrac{1}{2}\right)^2.\left(\dfrac{1}{2}+3.\dfrac{4}{9}\right)=\dfrac{55}{36}\)
+) \(C=2x+xy^2-x^2y-y\)
\(C=\left(2x+xy^2\right)-\left(x^2y+y\right)=x\left(2+y^2\right)-y\left(x^2+1\right)\)
Tại x= -1/2, y = -1/3 ta có :
\(C=\left(\dfrac{-1}{2}\right)\left[2+\left(\dfrac{-1}{3}\right)^2\right]-\left(-\dfrac{1}{3}\right)\left[\left(\dfrac{-1}{2}\right)^2+1\right]=\left(-\dfrac{19}{18}\right)-\left(-\dfrac{5}{12}\right)=\dfrac{-23}{36}\)
a) \(=5x^2+40x+80+4\left(x^2-10x+25\right)-9\left(x+4\right)\left(x-4\right)\)
\(=5x^2+40x+80+4x^2-40x+100-9x^2+144\)
\(=9x^2-9x^2+40x-40x+324\)
\(=324\)
b) \(=x^2+4xy+4y^2+4x^2-4xy+y^2-5x^2+5y^2-10y^2+90\)
\(=5x^2-5x^2+10y^2-10y^2+\left(4xy-4xy\right)+90\)
\(=90\)
c)
\(=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2+2ab-2ac-2bc-2a^2-4ab-2b^2\)
\(=\left(2a^2-2a^2\right)+\left(2b^2-2b^2\right)+2c^2+4ab-4ab+2\left(ac+bc-ac-bc\right)\)
\(=2c^2\)
a) 5( x + 4 )2 + 4( x - 5 )2 - 9( 4 + x )( x - 4 )
= 5( x2 + 8x + 16 ) + 4( x2 - 10x + 25 ) - 9( x2 - 16 )
= 5x2 + 40x + 80 + 4x2 - 40x + 100 - 9x2 + 144
= ( 5x2 + 4x2 - 9x2 ) + ( 40x - 40x ) + ( 80 + 100 + 144 )
= 324
b) ( x + 2y )2 + ( 2x - y )2 - 5( x + y )( x - y ) - 10( y + 3 )( y - 3 )
= x2 + 4xy + 4y2 + 4x2 - 4xy + y2 - 5( x2 - y2 ) - 10( y2 - 9 )
= x2 + 4xy + 4y2 + 4x2 - 4xy + y2 - 5x2 + 5y2 - 10y2 + 90
= ( x2 + 4x2 - 5x2 ) + ( 4xy - 4xy ) + ( 4x2 + y2 + 5y2 - 10y2 ) + 90
= 90
c) ( a + b + c )2 + ( a + b - c )2 - 2( a + b )2
= [ ( a + b ) + c ]2 + [ ( a + b ) - c ]2 - 2( a + b )2
= ( a + b )2 + 2( a + b )c + c2 + ( a + b )2 - 2( a + b )c + c2 - 2( a + b )2
= [ ( a + b )2 + ( a + b )2 - 2( a + b )2 ] + [ 2( a + b )c - 2( a + b )c ] + ( c2 + c2 )
= 2c2
a) (x + 2)(2 - x) - (2x - 1)(x + 3)
= 4 - x2 - 2x2 - 5x + 3
= -3x2 - 5x + 7
b) (x + 1)2 - 2(x2 - 1) + (x - 1)2
= (x + 1)2 - 2(x - 1)(x + 1) + (x - 1)2
= (x + 1 - x + 1)2
= 22 = 4
c) (x + y)3 - (x - y)2 - 6x2y
= x3 + 3x2y + 3xy2 + y3 - x3 + 3x2y - 3xy2 + y3 - 6x2y
= 2y3