1:

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

\(=4x^2-20x+25-4x^2-12x\)

=-32x+25

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

\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)

\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)

c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)

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

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

\(=9+10x-15=10x-6\)

2: 

a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)

\(=9x^2-12x+4-5x^2+20x+4x-4\)

\(=4x^2+12x\)

b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)

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

\(=-9x^2+27x\)

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

\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)

\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)

\(=-5\left(x^2-16\right)=-5x^2+80\)

Bài 2:

a: 2/6x5/3=10/18=5/9

b: 11/9x5/10=55/90=11/18

c: 3/9x6/8=1/3x3/4=1/4

d: 4/9x12/16=48/144=1/3

e: 25/15x6/7=5/3x6/7=30/21=10/7

f: 6/10x15/20=90/200=9/20

Bài 1

4/5 x 6/7= 24/35

2/9 x 1/2= 2/18= 1/9

1/2 x 8/3= 8/6= 4/3

7/9 x 6/5= 42/45= 14/15

8/7 x 5/9= 40/63

10/11 x 22/15= 220/165= 4/3

Bài 2

2/6 x 5/3= 1/3 x 5/3=5/9

11/9 x 5/10= 11/9 x 1/2= 11/18

3/9 x 6/8= 1/3 x 3/4 =3/12= 1/4

4/9 x 12/16= 4/9 x 3/4= 12/36= 1/3

25/15 x 6/7= 5/3 x 6/7= 30/21= 10/7

6/10 x 15/20= 3/5 x 3/4= 9/20

bài 1

4/5 x 6/7 = 24/35

2/9 x 1/2 = 1/9

1/2 x 8/3 = 4/3

7/9 x 6/5 = 14/15

8/7 x 5/9 = 14/15

8/7 x 5/9 = 40/63

10/11 x 22/15 = 4/3

a) ( x + 2 )( x + 3 ) - ( x - 2 )( x + 5 )

= x² + 5x + 6 - ( x² + 3x - 10 )

= x² + 5x + 6 - x² - 3x + 10

= 2x + 16

b) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10

= -5x² - 2x + 16 + 4( x² - x - 2 ) + 2( x² - 4 ) + 10

= -5x² - 2x + 16 + 4x² - 4x - 8 + 2x² - 8 + 10

= x² - 6x + 10

c) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )

= 4( x² + 4x - 5 ) - ( x² + 7x + 10 ) - 3( x² + x - 2 )

= 4x² + 16x - 20 - x² - 7x - 10 - 3x² - 3x + 6

= 6x - 24

d) ( x - 1 )( x⁵ + x⁴ + x³ + x² + x + 1 )

= x⁶ + x⁵ + x⁴ + x³ + x² + x - x⁵ - x⁴ - x³ - x² - x - 1

= x⁶ - 1

ai giúp mình với

a) \(\left(x-1\right)^2-\left(x+3\right)^2+\left(x+4\right)\left(x-4\right)\)

\(=x^2-2x+1-\left(x^2+6x+9\right)+x^2-16\)

\(=x^2-2x+1-x^2-6x-9+x^2-16=-8x-24\)

b)

\(2\left(3x-2\right)^2-3\left(2x+5\right)^2-6\left(x+1\right)\left(x-1\right)\)

\(=2\left(9x^2-12x+4\right)-3\left(4x^2+20x+25\right)-6\left(x^2-1\right)\)

\(=18x^2-24x+8-12x^2-60x-75-6x^2+6=-84x-61\)

a: \(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{6}{\sqrt{x}-1}-\dfrac{2\sqrt{3}}{\sqrt{x}-1}\)

\(=\dfrac{\sqrt{x}-6-2\sqrt{3}}{\sqrt{x}-1}\)

b: \(=\dfrac{3-\sqrt{x}-1+\sqrt{x}+5\sqrt{x}}{\sqrt{x}-2}=\dfrac{5\sqrt{x}+2}{\sqrt{x}-2}\)

c: \(=\dfrac{2-6\sqrt{x}-1+\sqrt{x}-3+\sqrt{x}}{\sqrt{x}-4}\)

\(=\dfrac{-4\sqrt{x}-4}{x-4}\)

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

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

\(=2x^2+3x^2-3-5x^2-5x\)

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

\(=-5x-3\)

b,c mk ms học lớp 7

Nhập biểu thức ở dấu Σ cho dễ nhìn em ạ

\(P=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{2x}{9-x}\right):\left(\dfrac{\sqrt{x}-1}{x-3\sqrt{x}}-\dfrac{2}{\sqrt{x}}\right)\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)-2x}{x-9}:\dfrac{\sqrt{x}-1-2\sqrt{x}+6}{\sqrt{x}\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-x-3\sqrt{x}}{x-9}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{-\sqrt{x}+5}\)

\(=\dfrac{-\sqrt{x}\left(\sqrt{x}+3\right)\cdot\sqrt{x}\left(\sqrt{x}-3\right)}{\left(x-9\right)\left(-\sqrt{x}+5\right)}=\dfrac{-x}{-\sqrt{x}+5}\)

\(A=\left(\dfrac{\sqrt{x}-2}{\sqrt{x}+5}+\dfrac{\sqrt{x}}{\sqrt{x}-5}+\dfrac{x+9}{25-x}\right):\dfrac{1-\sqrt{x}}{5+\sqrt{x}}\)

\(=\dfrac{x-7\sqrt{x}+10+x+5\sqrt{x}-x-9}{\left(x-25\right)}\cdot\dfrac{\sqrt{x}+5}{1-\sqrt{x}}\)

\(=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-5\right)\left(1-\sqrt{x}\right)}=\dfrac{1-\sqrt{x}}{\sqrt{x}-5}\)

\(B=\left(\dfrac{1}{x-4}-\dfrac{1}{x-4\sqrt{x}+4}\right):\dfrac{\sqrt[2]{x}}{2\sqrt{x}-x}\)

\(=\dfrac{\sqrt{x}-2-\sqrt{x}-2}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\dfrac{-\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}}\)

\(=\dfrac{-4}{x-4}\)