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1)a)3(2x-1)(3x-1)-(2x-3)(9x-1)=0
<=>18x2-15x+1-18x2+29x-3=0
<=>14x-2=0
<=>14x=2
<=>x=1/7
b)4(x+1)2+(2x-1)2-8(x-1)(x+1)=11
<=>4x2+8x+4+4x2-4x+1-8x2+8=11
<=>4x+13=11
<=>4x=11-13
<=>4x=-2
<=>x=-1/2
c)Sai đề phải là dấu - chứ không phải +
(x-3)(x2+3x+9)-x(x-2)(x+2)=1
<=>x3-27-x3+4x=1
<=>4x=1+27
<=>4x=28
<=>x=7
2)a)(2x-3y)(2x+3y)-4(x-y)2-8xy
=4x2-9y2-4x2+8xy-4y2-8xy
=-13y2
b)(x-2)3-x(x+1)(x-1)+6x(x-3)
=x3-6x2+12x+8-x3+x+6x2-18x
=8-5x
c)(x-2)(x2-2x+4)(x+2)(x2+2x+4)
=(x-2)(x2+2x+4)(x+2)(x2-2x+4)
=(x3-8)(x3+8)
=x6-64
a) x(2x^2 -3) -x^2 (5x+1 ) + x^2
<=> 2x^3 -3x -5x^3 -x^2 +x^2
<=>3x^3 -3x
b) 3x(x-2) -5x(1-x)-8(x^2 -3)
=3x^2 -6x -5x +5x^2 -8x^2 +24
= -11x+24
Rút gọn biểu thức
a).x(2x2-3)-x2(5x+1)+x2
b).3x(x-2)-5x(1-x)-8(x2-3)
c).1/2x2(6x-3)-x(x2+1/2)+1/2(x+4)
bài 1.
a.\(A=x^2-2xy+y^2+x^2+2xy+y^2=2\left(x^2+y^2\right)\)
b.\(B=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)=4xy\)
c.\(C=4a^2+4ab+b^2-\left(4a^2-4ab+b^2\right)=8ab\)
d.\(D=4x^2-4x+1-2\left(4x^2-12x+9\right)+4=-4x^2+20x-13\)
.bài 2
a.\(A=x^2+6x+9+x^2-9-2\left(x^2-2x-8\right)=10x+16;x=-\frac{1}{2}\Rightarrow A=9\)
b.\(B=9x^2+24x+16-x^2+16-10x=8x^2+14x+32\Rightarrow x=-\frac{1}{10}\Rightarrow B=\frac{767}{25}\)
c.\(C=x^2+2x+1-\left(4x^2-4x+1\right)+3\left(x^2-4\right)=6x-12\Rightarrow x=1\Rightarrow C=-6\)
d.\(D=x^2-9+x^2-4x+4-2x^2+8x=4x-5\Rightarrow x=-1\Rightarrow A=-9\)
Trả lời:
Bài 1: Rút gọn biểu thức:
a) A = ( x - y )2 + ( x + y )2
= x2 - 2xy + y2 + x2 + 2xy + y2
= 2x2 + 2y2
b) B = ( x + y )2 - ( x - y )2
= x2 + 2xy + y2 - ( x2 - 2xy + y2 )
= x2 + 2xy + y2 - x2 + 2xy - y2
= 4xy
c) C = ( 2a + b )2 - ( 2a - b )2
= 4a2 + 4ab + b2 - ( 4a2 - 4ab + b2 )
= 4a2 + 4ab + b2 - 4a2 + 4ab - b2
= 8ab
d) D = ( 2x - 1 )2 - 2 ( 2x - 3 )2 + 4
= 4x2 - 4x + 1 - 2 ( 4x2 - 12x + 9 ) + 4
= 4x2 - 4x + 1 - 8x2 + 24x - 18 + 4
= - 4x2 + 20x - 13
Bài 2: Rút gọn rồi tính giá trị biểu thức:
a) A = ( x + 3 )2 + ( x - 3 )( x + 3 ) - 2 ( x + 2 )( x - 4 )
= x2 + 6x + 9 + x2 - 9 - 2 ( x2 - 2x - 8 )
= 2x2 + 6x - 2x2 + 4x + 16
= 10x + 16
Thay x = 1/2 vào A, ta có:
\(A=10.\left(-\frac{1}{2}\right)+16=-5+16=11\)
b) B = ( 3x + 4 )2 - ( x - 4 )( x + 4 ) - 10x
= 9x2 + 24x + 16 - x2 + 16 - 10x
= 8x2 + 14x + 32
Thay x = - 1/10 vào B, ta có:
\(B=8.\left(-\frac{1}{10}\right)^2+14.\left(-\frac{1}{10}\right)+32=\frac{767}{25}\)
c) C = ( x + 1 )2 - ( 2x - 1 )2 + 3 ( x - 2 )( x + 2 )
= x2 + 2x + 1 - 4x2 + 4x - 1 + 3 ( x2 - 4 )
= - 3x2 + 6x + 3x2 - 12
= 6x - 12
Thay x = 1 vào C, ta có:
\(C=6.1-12=-6\)
d) D = ( x - 3 )( x + 3 ) + ( x - 2 )2 - 2x ( x - 4 )
= x2 - 9 + x2 - 4x + 4 - 2x2 + 8x
= 4x - 5
Thay x = - 1 vào D, ta có:
\(D=4.\left(-1\right)-5=-9\)
b) \(3x\left(x-1\right)^2-2x\left(x+3\right)\left(x-3\right)+4x\left(x-4\right)\)
\(=3x\left(x^2-2x+1\right)-2x\left(x^2-9\right)+4x^2-16x=3x^3-6x^2+3x-2x^3+18x+4x^2-16x\)\(=x^3-2x^2+5x\)
c) \(2\left(2x+5\right)^2-3\left(4x+1\right)\left(1-4x\right)=2\left(4x^2+20x+25\right)+3\left(16x^2-1\right)\)
\(=8x^2+40x+50+48x^2-3=56x^2+40x+47\)
d) \(x\left(x+4\right)\left(x-4\right)-\left(x^2+1\right)\left(x^2-1\right)=x\left(x^2-16\right)-x^4+1=x^3-x^4-16x+1\)
e) \(\left(y-3\right)\left(y+3\right)\left(y^2+9\right)-\left(y^2+2\right)\left(y^2-2\right)=\left(y^2-9\right)\left(y^2+9\right)-y^4+4=y^4-81-y^2+4=-77\)
a) [ a^2+b^2+c^2-2ab-2bc+2ac]--(b^2-2bc+c^2)+2ab-2ac
=a^2+b^2+c^2-2ab-2bc+2ac-b^2+2bc-c^2+2ab+2ac
=a^2
b) (x^3-6x^2+12x-8)-x(x^2-1)+6x^2-18x
=x^3-6x^2+12x-8-x^3+x+6x^2-18x
= -5x-8