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20 tháng 7 2017

1)

(x-3).(x+3) - (x+1)2

= x2 - 32 - x2 - 2x - 1

= - 2x - 10

2)

(2x - 1)2 - (x +2)2 - (2x - \(\dfrac{1}{2}\))2

= 4x2 - 4x +1 - x2 - 4x - 4 - 4x2 + 2x - \(\dfrac{1}{4}\)

= - x2 - 6x - \(\dfrac{13}{4}\)

= - ( x2 + 6x + \(\dfrac{13}{4}\) )

= - (x2 + 2.3x + 9 - \(\dfrac{23}{4}\))

= - (x + 3)2 + \(\dfrac{23}{4}\)

3)

(2x + 1)3 - (2x -1)3 - 24x2

= (2x -1 + 2)3 - (2x - 1)3 - 24x2

= (2x-1)3 + 3.(2x-1)2.2 + 3.(2x-1).22 + 23 - (2x - 1)3 - 24x2

= 6.(4x2 - 4x + 1) + 24x - 12 +8 - 24x2

= 24x2 - 24x + 6 +24x - 4 - 24x2

= 2

4)

(x-2)3 - (2x + 3)3 - 7.(1 - x)3

= x3 - 3.x2.2 + 3x.22 - 23 - 8x3 + 3.4x2.3 - 3.2x.32 + 33 - 7.(13-3x + 3x2 - x3)

= x3 - 3.x2.2 + 3x.22 - 23 - 8x3 + 3.4x2.3 - 3.2x.32 + 33 - 7 + 21x - 21x2 + 7x3

= x3 - 6x2 + 12x - 8 - 8x3 + 36x2 - 54x2 + 27 - 7 + 21x - 21x2 + 7x3

= - 45x2 + 33x + 12

= - 45(x2 - \(\dfrac{33}{45}x-\dfrac{4}{15}\))

= \(-45.\left(x^2-2.\dfrac{11}{30}.x+\dfrac{121}{900}-\dfrac{361}{900}\right)\)

= \(-45.\left(x-\dfrac{11}{30}\right)^2+\dfrac{361}{20}\)

1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)

\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)

\(=-63x^2-21x-42\)

2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)

3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)

19 tháng 7 2017

Như thế này bn thấy rõ k

Những hằng đẳng thức đáng nhớ

20 tháng 7 2017

Trai Vô Đối cái phần 2 dòng 2 đoạn cuối là j vậy

1:  \(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-2\left(4x+3\right)^2+8\left(x+3\right)^2\)

\(=24x^2+2-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)

\(=24x^2+2-32x^2-48x-18+8x^2+48x+72\)

=56

2: \(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(3-2x\right)\left(3+x\right)-\left(3x-3\right)^2\)

\(=4x^3-3x-1-2x^3+12x^2-24x+16+x\left(9-3x-2x^2\right)-\left(3x-3\right)^2\)

\(=2x^3+12x^2-27x+15+9x-3x^2-2x^3-9x^2+18x-9\)

\(=6\)

20 tháng 7 2017

1. \(\left(x+5\right)\left(x^2-5x+25\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3+125-\left(x^3-8\right)=x^3+125-x^3+8=133\)

20 tháng 7 2017

1,

\(\left(x+5\right)\left(x^2-5x+25\right)-\left(x-2\right)\left(x^2+2x+4\right)\\ =\left(x^3+5^3\right)-\left(x^3-2^3\right)\\ =x^3+125-x^3+8\\ =\left(x^3-x^3\right)+\left(125+8\right)\\ =133\)

b,

\(\left(2x-3\right)\left(4x^2+6x+9\right)-\left(2x+1\right)^3\\ =\left[\left(2x\right)^3-3^3\right]-\left[\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x+1+1\right]\\ =\left(8x^3-27\right)-\left(8x^3+12x^2+6x+1\right)\\ =8x^3-27-8x^3-12x^2-6x-1\\ =\left(8x^3-8x^3\right)-\left(12x^2+6x\right)-\left(27+1\right)\\ =-6x\left(2x+1\right)-28\\ =\left(-2\right)\left[3x\left(2x+1\right)+14\right]\)

a: \(P=\left(\dfrac{3x+6}{2\left(x^2+4\right)}-\dfrac{2x^2-x-10}{\left(x+1\right)\left(x^2+1\right)}\right):\left(\dfrac{10\left(x^2-1\right)+3\left(x^2+1\right)\left(x-1\right)-6\left(x+1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\cdot2}\right)\cdot\dfrac{2}{x-1}\)

\(=\left(\dfrac{\left(3x+6\right)\left(x^3+x^2+x+1\right)-\left(2x^2+8\right)\left(2x^2-x-10\right)}{2\left(x^2+4\right)\left(x+1\right)\left(x^2+1\right)}\right)\cdot\dfrac{\left(x^2+1\right)\left(x-1\right)\left(x+1\right)\cdot2}{-3x^3+x^2-3x-13}\cdot\dfrac{2}{x-1}\)

\(=\dfrac{-x^4+11x^3+13x^2+17x+16}{\left(x^2+4\right)}\cdot\dfrac{2}{-3x^3+x^2-3x-13}\)

20 tháng 7 2017

phá hằng đẳng thức là ra bn

20 tháng 7 2017

a,Ta có

x-3+x+3-(x\(^2\)+2x+1)=2x-x\(^2\)-2x-1=-x\(^2\)-1

b Ta có

4x^2-4x+1-(x^2+4x+4)-(4x^2-2x+1/4)=4x^2-4x+1-x^2-4x-4-4x^2+2x-1/4=-6x-x^2-13/4=(x+3)^2-23/4

c,Ta có

8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-24x^2=1+1=2

15 tháng 6 2018

1> 3x(x-2)-2x(2x-1)=(1-x)(1+x)

\(3x^2\)-6x-\(4x^2\)+2x=1-\(x^2\)

⇔-1\(x^2\) - 4x= 1- \(x^2\)

⇔ -1\(x^2\) -4x+ \(x^2\) = 1

⇔-4x=1

⇔ x = \(\dfrac{-1}{4}\)

21 tháng 7 2017

1. (2x - 3) . (2x+3) - 4 . (x+ 2)2 = 6

[ ( 2x )2 - 32 ] - 4 . ( x2 + 2.x.2 + 22) = 6

4x2 - 9 - 4 . ( x2 + 4x + 4) = 6

4x2 - 9 - 4x2 - 16x - 16 = 6

-16x -25 = 6

x = \(-\dfrac{31}{16}\)

24 tháng 5 2018

1.\(\left(x-5\right).\left(x+5\right)-\left(x+3\right)^2=2x-3\)

\(\Leftrightarrow x^2-25-\left(x^2+6x+9\right)=2x-3\)

\(\Leftrightarrow x^2-25-x^2-6x-9=2x-3\)

\(\Leftrightarrow x^2-25-x^2-6x-9-2x+3=0\)

\(\Leftrightarrow-8x-31=0\)

\(\Leftrightarrow x=\dfrac{-31}{8}\)

24 tháng 5 2018

\(\left(x-4\right)^3-\left(x-5\right)\left(x^2+5x+25\right)=\left(x+2\right)\left(x^2-2x+4\right)-\left(x+4\right)^3\)

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

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

\(\Leftrightarrow\left(x^3-12x^2+48x-64\right)-x^3+5^3=x^3+2^3-\left(x^3+12x^2+48x+64\right)\)

\(\Leftrightarrow x^3-12x^2+48x-64-x^3+5^3=x^3+2^3-x^3-12x^2-48x-64\)

\(\Leftrightarrow-12x^2+48x-64+5^3=2^3-12x^2-48x-64\)

\(\Leftrightarrow-12x^2+48x-61=-12x^2-48x-56\)

\(\Leftrightarrow96x=-117\)

\(\Leftrightarrow x=\dfrac{-117}{96}=\dfrac{-39}{32}\)