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

Toán Lớp 8: $Bài$ $1$: $Rút$ $gọn$ $biểu$ $thức$ $a)$ $(x+3)$ $.$ $(x^{2}$ $+$ $3x$ $+$ $9$) $-$ $(54$ $+$ $x^{3}$ $)$ $b)$ ($2x$ $+$ $y$ $)$ $.$ $

Toán Lớp 8: $Bài$ $1$: $Rút$ $gọn$ $biểu$ $thức$
$a)$ $(x+3)$ $.$ $(x^{2}$ $+$ $3x$ $+$ $9$) $-$ $(54$ $+$ $x^{3}$ $)$
$b)$ ($2x$ $+$ $y$ $)$ $.$ $($ $4x^{2}$ $-$ $2y$ $+$ $y^{2}$ $)$ $-$ $($ $2x$ $-$ $y$ $)$ $.$ $($$4x^{2}$ $+$ $2xy$ $+$ $y^{2}$ $)$

Comments ( 2 )

  1. a)(x+3)(x^2+3x+9)-(54+x^3)
    =x^3+3x^2+9x+3x^2+9x+27-54-x^3
    =(x^3-x^3)+(3x^2+3x^2)+(9x+9x)+(27-54)
    =6x^2+18x-27
    Sửa đề:(x+3)(x^2+3x+9)-(54+x^3)
    →(x+3)(x^2-3x+9)-(54+x^3)
    (x+3)(x^2-3x+9)-(54+x^3)
    =(x+3)(x^2-x.3+3^2)-54-x^3
    =x^3+3^3-54-x^3
    =x^3+27-54-x^3
    =(x^3-x^3)+(27-54)
    =-27
    b)(2x+y)(4x²-2y+y²)-(2x-y)(4x²+2xy+y²)
    =8x³-4xy+2xy²+4x²y-2y²+y³-(2x-y)[(2x)²+2x.y+y²]
    =8x³-4xy+2xy²+4x²y-2y²+y³-[(2x)³-y³]
    =8x³-4xy+2xy²+4x²y-2y²+y³-(8x³-y³)
    =8x³-4xy+2xy²+4x²y-2y²+y³-8x³+y³
    =(8x³-8x³)-4xy+2xy²+4x²y-2y²+(y³+y³)
    =-4xy+2xy²+4x²y-2y²+2y³
    Sửa đề:(2x+y)(4x²-2y+y²)-(2x-y)(4x²+2xy+y²)
    →(2x+y)(4x²-2xy+y²)-(2x-y)(4x²+2xy+y²)
    (2x+y)(4x²-2xy+y²)-(2x-y)(4x²+2xy+y²)
    =(2x+y)[(2x)²-2x.y+y²]-(2x-y)[(2x)²+2x.y+y²]
    =(2x)³+y³-[(2x)³-y³]
    =8x³+y³-(8x³-y³)
    =8x³+y³-8x³+y³
    =(8x³-8x³)+(y³+y³)
    =2y³

  2. a)
    (x+3)(x^2- 3x+9) – (54+x^3)
    =  (x+3)(x^2 – x . 3 + 3^2) – (54 + x^3)
    =  (x^3 + 3^3) – (54 + x^3)
    = (x^3 + 27) – (54 +x^3)
    = x^3 + 27 – 54-  x^3
    =  (x^3 – x^3) + (27-54)
    =  -27
    (x+3)(x^2 + 3x+9) – (54 + x^3)
    =  (x^3 + 3x^2 + 9x + 3x^2 + 9x + 27) – (54+x^3)
    =  x^3 + 3x^2 + 9x + 3x^2 + 9x + 27 – 54 – x^3
    = (x^3 – x^3) + (3x^2 + 3x^2) + (9x+9x) + (27-54)
    =  6x^2 + 18x -27
    b)
    (2x+y)(4x^2 – 2xy + y^2) – (2x-y)(4x^2 + 2xy + y^2)
    =  (2x+y) [ (2x)^2 – 2x . y + y^2] – (2x-y) [ (2x)^2 + 2x . y + y^2]
    = [(2x)^3 + y^3] – [ (2x)^3 – y^3]
    =  (8x^3 + y^3) – (8x^3 -y^3)
    =  8x^3 + y^3 – 8x^3 + y^3
    = (8x^3-8x^3) + (y^3+y^3)
    = 2y^3
    (2x+y)(4x^2 – 2y + y^2) – (2x-y)(4x^2 + 2xy + y^2)
    = (8x^3 – 4xy + 2xy^2 + 4x^2y – 2y^2 + y^3) – (2x-y) [ (2x)^2 + 2x . y + y^2]
    =  (8x^3 – 4xy + 2xy^2 + 4x^2y – 2y^2 + y^3) – [ (2x)^3 – y^3]
    =  (8x^3 – 4xy + 2xy^2 + 4x^2y – 2y^2 + y^3) – (8x^3 – y^3)
    =  8x^3 – 4xy + 2xy^2 + 4x^2y – 2y^2 + y^3-  8x^3 + y^3
    =  (8x^3 – 8x^3) + (y^3 + y^3) – 4xy + 2xy^2 + 4x^2y – 2y^2
    =  2y^3 – 4xy + 2xy^2 + 4x^2y – 2y^2
     

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