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13 tháng 7 2016

Bài 1:

a) \(\left(a+b\right)^2-\left(a-b\right)^2\)

\(=\left(a+b+\left(a-b\right)\right).\left(a+b-\left(a-b\right)\right)\)

\(=2a.2b\)

\(=4ab\)

13 tháng 7 2016

Câu 1:

a) (a +b )2 - ( a -b )2

=a2+b2-a2+b2

=2b2

 b) (a + b )3- ( a - b )3 - 2b3

=a3+b3-a+b3-2b3

=a3-a

c) ( x+y+z)2 - 2(x+y+z)(x+y) + (x + y )2

=x2+xy+xz+xy+y2+yz+xz+yz+z2-2.(x2+xy+xz+xy+y2+yz)+x2+xy+xy+y2

=x2+y2+z2+2xy+2xz+2yz-2x2-2y2-4xy-2xz-2yz+x2+2xy+y2

=0

15 tháng 7 2021

B1

a, \(=>A=\left(x+y+x-y\right)\left(x+y-x+y\right)=2x.2y=4xy\)

b, \(=>B=\left[\left(x+y\right)-\left(x-y\right)\right]^2=\left[x+y-x+y\right]^2=\left[2y\right]^2=4y^2\)

c,\(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)

\(=\)\(\left(x+1\right)\left(x^2-x+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^3+1^3\right)\left(x^3-1^3\right)=x^6-1\)

d, \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)

\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a-b+c\right)^2-\left(b-c\right)^2\)

\(=\left(a+b-c+b-c\right)\left(a+b-c-b+c\right)\)

\(+\left(a-b+c+b-c\right)\left(a-b+c-b+c\right)\)

\(=a\left(a+2b-2c\right)+a\left(a-2b\right)\)

\(=a\left(a+2b-2c+a-2b\right)=a\left(2a-2c\right)=2a^2-2ac\)

B2:

\(\)\(x+y=3=>\left(x+y\right)^2=9=>x^2+2xy+y^2=9\)

\(=>xy=\dfrac{9-\left(x^2+y^2\right)}{2}=\dfrac{9-\left(17\right)}{2}=-4\)

\(=>x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3\left(17+4\right)=63\)

Bài 1: 

a) Ta có: \(\left(x+y\right)^2-\left(x-y\right)^2\)

\(=x^2+2xy+y^2-x^2+2xy+y^2\)

=4xy

b) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)

\(=\left(x+y-x+y\right)^2\)

\(=\left(2y\right)^2=4y^2\)

c) Ta có: \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)

\(=\left(x^3-1\right)\left(x^3+1\right)\)

\(=x^6-1\)

d) Ta có: \(\left(a+b-c\right)^2+\left(a+b+c\right)^2-2\left(b-c\right)^2\)

\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a+b+c\right)^2-\left(b-c\right)^2\)

\(=\left(a+b-c-b+c\right)\left(a+b-c+b-c\right)+\left(a+b+c-b+c\right)\left(a+b+c+b-c\right)\)

\(=a\cdot\left(a+2b-2c\right)+\left(a+2c\right)\left(a-2b\right)\)

\(=a^2+2ab-2ac+a^2-2ab+2ac-4bc\)

\(=2a^2-4bc\)

26 tháng 12 2017

10 tháng 12 2020

a) \(\left(x^5+4x^3-6x^2\right):4x^2\)

\(=\left(x^5:4x^2\right)+\left(4x^3:4x^2\right)+\left(-6x^2:4x^2\right)\)

\(=\dfrac{1}{4}x^3+x-\dfrac{3}{2}\)

b)  x^3 + x^2 - 12 x-2 x^3 - 2x^2 3x^2 - 12 3x^2 - 6x 6x - 12 x^2+3x+6 6x - 12 0

Vậy \(\left(x^3+x^2-12\right):\left(x-2\right)=x^2+3x+6\)

c) (-2x5 : 2x2) + (3x2 : 2x2) + (-4x^3 : 2x^2)

\(-x^3+\dfrac{3}{2}-2x\)

d) \(\left(x^3-64\right):\left(x^2+4x+16\right)\)

\(=\left(x-4\right)\left(x^2+4x+16\right):\left(x^2+4x+16\right)\)

\(=x-4\)

(dùng hẳng đẳng thức thứ 7)

Bài 2 :

a) 3x(x - 2) - 5x(1 - x) - 8(x2 - 3)

= 3x2 - 6x - 5x + 5x2 - 8x2 + 24

= (3x2 + 5x2 - 8x2) + (-6x - 5x) + 24 

= -11x + 24

b) (x - y)(x2 + xy + y2) + 2y3

= x3 - y3 + 2y3

= x3 + y3 

c) (x - y)2 + (x + y)2 - 2(x - y)(x + y)

= (x - y)2 - 2(x - y)(x + y) + (x + y)2

= [(x - y) + x + y)2 = [x - y + x + y] = (2x)2 = 4x2

 

18 tháng 10 2021

Bài 1 :

a]=  \(\frac{1}{4}\)x3 + x - \(\frac{3}{2}\).

b] => [x3 + x2 -12 ] = [ x2 +3 ][x-2] + [-6]

c]= -x3 -2x +\(\frac{3}{2}\).

d] = [ x3 - 64 ]  = [ x2 + 4x + 16][ x- 4].

Bài 4: 

b: \(=x^2z\left(-1+3-7\right)=-5x^2z=-5\cdot\left(-1\right)^2\cdot\left(-2\right)=10\)

c: \(=xy^2\left(5+0.5-3\right)=2.5xy^2=2.5\cdot2\cdot1^2=5\)

23 tháng 2 2022

a, \(A=2x^2+x+6\)

Với x = 1 suy ra A = 2 + 1 + 6 = 9 

Với x = 1/2 suy ra A = 1/2 + 1/2 + 6 = 7 

b, \(B=7x-6y-5\)Thay x = 3 ; y = -2 ta được 

B = 7.3 - 6 ( - 2 ) - 5 = 21 + 12 - 5 = 33 - 5 = 28 

13 tháng 9 2018

chỉ đi

9 tháng 9 2021

\(1,\\ a,A=4x^2\left(-3x^2+1\right)+6x^2\left(2x^2-1\right)+x^2\\ A=-12x^4+4x^2+12x^2-6x^2+x^2=-x^2=-\left(-1\right)^2=-1\\ b,B=x^2\left(-2y^3-2y^2+1\right)-2y^2\left(x^2y+x^2\right)\\ B=-2x^2y^3-2x^2y^2+x^2-2x^2y^3-2x^2y^2\\ B=-4x^2y^3-4x^2y^2+x^2\\ B=-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^3-4\left(0,5\right)^2\left(-\dfrac{1}{2}\right)^2+\left(0,5\right)^2\\ B=\dfrac{1}{8}-\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{8}\)

9 tháng 9 2021

\(2,\\ a,\Leftrightarrow10x-16-12x+15=12x-16+11\\ \Leftrightarrow-14x=-4\\ \Leftrightarrow x=\dfrac{2}{7}\\ b,\Leftrightarrow12x^2-4x^3+3x^3-12x^2=8\\ \Leftrightarrow-x^3=8=-2^3\\ \Leftrightarrow x=2\\ c,\Leftrightarrow4x^2\left(4x-2\right)-x^3+8x^2=15\\ \Leftrightarrow16x^3-8x^2-x^3+8x^2=15\\ \Leftrightarrow15x^3=15\\ \Leftrightarrow x^3=1\Leftrightarrow x=1\)

 

10 tháng 7 2016

Bài 1:

  • a,(2+xy)^2=4+4xy+x^2y^2
  • b,(5-3x)^2=25-30x+9x^2
  • d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1