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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Bài 1: Rút gọn các biểu thức sau: a) 5(2x – 1) – 2(5x + 3) b) 3(x + y) – 3(x – 2xy + y) c)

Toán Lớp 8: Bài 1: Rút gọn các biểu thức sau:
a) 5(2x – 1) – 2(5x + 3)
b) 3(x + y) – 3(x – 2xy + y)
c) (2x + 1)2 + (2x – – 2(1 + 2x)(2x – 1)
d) (x + 1)(x2 – x + 1) – x(x + 4)(x – 4)

Comments ( 2 )

  1. a)
    5 (2x-1) – 2 (5x+3)
    = 5 . 2x – 5 . 1 – 2 . 5x – 2 . 3
    =  10x – 5 – 10x – 6
    = (10x-10x) – (5+6)
    = -11
    b)
    3 (x+y) – 3 (x-2xy + y)
    =  3 . x + 3 . y – 3 . x + 3 .2xy – 3 . y
    =3x + 3y – 3x + 6xy – 3y
    =  (3x-3x) + (3y-3y) + 6xy
    =  6xy
    c)
    (2x+1)^2 + (2x-1)^2 – 2 (1+2x)(2x-1)
    =  [ (2x+1) – (2x-1)]^2
    = (2x+1-2x+1)^2
    = 2^2
    = 4
    d)
    (x+1)(x^2 – x + 1) – x (x+4)(x-4)
    =  (x+1)(x^2 – x . 1 +1^2) – x (x^2 – 4^2)
    =  (x^3 + 1^3) – x (x^2 – 16)
    = x^3 + 1 – x^3 + 16x
      = 16x+1
     

  2. a) 5 ( 2x – 1 ) – 2 ( 5x + 3 )
    = 5 . 2x + 5 . ( – 1 ) – 2 . 5x – 2 . 3
    = 10x – 5 – 10x – 6
    = ( 10x – 10x ) + ( – 5 – 6 )
    = 0 – 11
    = – 11
    b) 3 ( x + y ) – 3 ( x – 2xy + y )
    = 3 . x + 3 . y – 3 . x – 3 . ( – 2xy ) – 3 . y
    = 3x + 3y – 3x + 6xy – 3y
    = ( 3x – 3x ) + ( 3y – 3y ) + 6xy
    = 0 + 0 + 6xy
    = 6xy
    c) ( 2x + 1 )^2 + ( 2x – 1 )^2 – 2 ( 1 + 2x ) ( 2x – 1 )
    = 4x^2 + 4x + 1 + 4x^2 – 4x + 1 – 2 ( 2x + 1 ) ( 2x + 1 )
    = 4x^2 + 1 + 4x^2 + 1 – 2 ( 4x^2 – 1 )
    = 8x^2 + 1 + 1 – 8x^2 + 2
    = ( 8x^2 – 8x^2 ) + 1 + 1 + 2
    = 0 + 2 + 2
    = 4
    d) ( x + 1 ) ( x^2 – x + 1 ) – x ( x + 4 ) ( x – 4 )
    = x^3 + 1 – x ( x^2 – 16 )
    = x^3 + 1 – x^3 + 16x
    = 1 + 16x

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222-9+11+12:2*14+14 = ? ( )

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