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

Toán Lớp 8: Rút gọn biểu thức: $( a + b – c)^{2}$ – $( a – b)^{2}$ – 2c(a + b)

Toán Lớp 8: Rút gọn biểu thức: $( a + b – c)^{2}$ – $( a – b)^{2}$ – 2c(a + b)

Comments ( 2 )

  1. Giải đáp:
    (a+b-c)^2 – (a-b)^2 – 2c (a+b) = c^2 + 4ab – 4ac – 4bc
    Lời giải và giải thích chi tiết:
     (a+b-c)^2 – (a-b)^2 – 2c (a+b)
    =  [(a+b) – c]^2 – (a^2 – 2ab + b^2) – (2ac + 2bc)
    = (a+b)^2 -2c(a+b) + c^2 – a^2 + 2ab – b^2 – 2ac – 2bc
    = a^2+ 2ab + b^2 – 2ac – 2bc + c^2 – a^2 + 2ab – b^2 – 2ac – 2bc
    = (a^2 -a^2)+ (b^2 – b^2) + c^2 + (2ab + 2ab) – (2ac + 2ac) – (2bc + 2bc)
    = c^2 + 4ab – 4ac – 4bc

  2. (a+b-c)^2 – (a-b)^2 – 2c(a+b)
    = (a+b)^2 -2(a+b)c + c^2 – a^2 +2ab – b^2 – 2ac – 2bc
    = a^2 + 2ab +b^2 – 2ac – 2bc +c^2 – a^2 +2ab – b^2 – 2ac – 2bc
    = (a^2-a^2)+(2ab+2ab) +(b^2-b^2) +(-2ac – 2ac) +(-2bc -2bc) +c^2
    = 4ab – 4ac – 4bc +c^2

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