20% dd

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Trả lời:

3, a³b - ab³ + a² + 2ab + b²

= ( a³b - ab³ ) + ( a² + 2ab + b² )

= ab ( a² - b² ) + ( a + b )²

= ab ( a - b )( a + b ) + ( a + b )²

= ( a + b )[ ab( a - b ) + a + b ]

= ( a + b )( a²b - ab² + a + b )

4, 2x³ - 2xy² - 8x² + 8xy 

= ( 2x³ - 2xy² ) - ( 8x² - 8xy )

= 2x ( x² - y² ) - 8x ( x - y )

= 2x ( x - y )( x + y ) - 8x ( x - y )

= ( x - y )[ 2x ( x + y ) - 8x ]

= ( x - y )( 2x² + 2xy - 8x )

= 2x ( x - y )( x + y - 4 )

mk cũng ko bt

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khó hiểu bạn ơi

1.a)A = (1 - 1/3)(1-2/5)...(1-5/5)....(1-9/5)

      =(1-1/3)....0.....(1-9/5)

      =0

     =>đpcm.

b)ta xét:

1/2² = 1/2x2 < 1/1x2

.............

1/8² = 1/8x8 <1/7x8

=>B < 1/1x2 + 1/2x3 ... + 1 + 1/7x8

<=> B <1 - 1/2 + 1/2  - 1/3  + ... + 1/7 - 1/8

<=> B < 1 - 1/8 = 7/8 < 1

=> B < 1 => đpcm

2.a) Đặt m = 2007(2006+2007) = 2006(2006 + 2007) + (2006+2007)

      Đặt n = 2006(2007+2008) = 2006(2006+2007) + (2006 + 2006)

Ta thấy : (2006+2007) > (2006 + 2006) => m > n , áp dụng công thức "a.d > c.d <=> a/b > b/d (a,c thuộc Z// b,d thuộc N)

=> A > B

   b)ta có: D = 196 + 197/197 + 198 = (196/197+198) + (197/197+198) < 196/197 + 197/198 = C

=> C > D

c)gọi 20¹⁰ là a

ta thấy : (a + 1)(a-3) = (a - 1)(a - 3) + 2(a - 3) < (a - 1)(a - 3) + 2(a - 1) = (a - 1)(a - 1)

áp dụng: ad > bc <=> a/b > c/d ( a,b,c,d thuộc Z// b,d > 0)

=> E > F

1 + 2xy - x² - y²

= 1 - ( x² - 2xy + y² )

= 1² - ( x - y )²

= [ 1 - ( x - y ) ][ 1 + ( x - y ) ]

= ( y - x + 1 )( x - y + 1 )

a² + b² - c² - d² - 2ab + 2cd

= ( a² - 2ab + b² ) - ( c² - 2cd + d² )

= ( a - b )² - ( c - d )²

= [ ( a - b ) - ( c - d ) ][ ( a - b ) + ( c - d ) ]

= ( a - b - c + d )( a - b + c - d )

a³b³ - 1

= ( ab )³ - 1³

= ( ab - 1 )[ ( ab )² + ab.1 + 1² ]

= ( ab - 1 )( a²b² + ab + 1 )

x²( y - z ) + y²( z - x ) + z²( x - y )

= z²( x - y ) + x²y - x²z + y²z + y²x

= z²( x - y ) + ( x²y - y²x ) - ( x²z - y²z )

= z²( x - y ) + xy( x - y ) - z( x² - y² )

= z²( x - y ) + xy( x - y ) - z( x + y )( x - y )

= ( x - y )[ z² + xy - z( x + y ) ]

= ( x - y )( z² + xy - zx - zy )

= ( x - y )[ ( z² - zx ) - ( zy - xy ) ]

= ( x - y )[ z( z - x ) - y( z - x ) ]

= ( x - y )( z - x )( z - y )

a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=7.\frac{5^8}{5^8}=7\)

b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3.3^8.5^2.5^3}{3.5.5^4.3^8}=\frac{5^5}{5^5}=1\)

c) Đề hơi sai roi bạn oi

d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{61}{50}\)

Khanh Nguyễn Ngọc  :câu d ko sai bạn nha dấu "/" là trên nhó

a) \(x^2-5x+6\)

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

b) \(x^2-9x+18=x^2-3x-6x+18\)

\(=x\left(x-3\right)-6\left(x-3\right)=\left(x-3\right)\left(x-6\right)\)

c) \(x^2-6x+5=x^2-x-5x+5\)

\(=x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(x-5\right)\)

d) \(3x^2+5x-30=3\left(x^2+\dfrac{5x}{3}-10\right)=3\left(x^2+2.x.\dfrac{5}{6}+\dfrac{25}{36}-\dfrac{5347}{500}\right)\)

Câu này bạn xem lại đề nha

e) \(3x^2-5x-2=3x^2-6x+x-2\)

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