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

Toán Lớp 8: Rút gọn a, (a+b+c)² – (a+b) ² – (a+c)² – (b+c)² b, (a+b+c)² + (a-b+c) ² + (a+b-c)² + (-a+b+c)²

Toán Lớp 8: Rút gọn
a, (a+b+c)² – (a+b) ² – (a+c)² – (b+c)²
b, (a+b+c)² + (a-b+c) ² + (a+b-c)² + (-a+b+c)²

Comments ( 2 )

  1. a, (a+b+c)² – (a+b) ² – (a+c)² – (b+c)²
    = a²+b²+c²+2ab+2bc+2ca-a²-2ab-b²-a²-2ac-c²-b²-2bc-c²
    =(a²+b²+c²-a²-b²-c²)+(2ab+2bc+2ac-2ab-2ac-2bc)-a²-b²-c²
    =-a²-b²-c²
    b)(a+b+c)² + (a-b+c) ² + (a+b-c)² + (-a+b+c)²
    =a²+b²+c²+2ab+2bc+2ca+a²+b²+c²-2ab-2bc+2ac+a²+b²+c²+2ab-2ac-2bc+(-a)²+b²+c²-2ab+2bc-2ca
    =4a²+4b²+4c² 
    =4(a²+b²+c²) 
     

  2. Giải đáp:
    a)-a²-b²-c²
    b)4a²+4b²+4c²
    Lời giải và giải thích chi tiết:
    a)(a+b+c)²-(a+b)²-(a+c)²-(b+c)²
    =[(a+b)+c]²-(a²+2ab+b²)-(a²+2ac+c²)-(b²+2bc+c²)
    =(a+b)²+2c(a+b)+c²-a²-2ab-b²-a²-2ac-c²-b²-2bc-c²
    =a²+2ab+b²+2ac+2bc+c²-a²-2ab-b²-a²-2ac-c²-b²-2bc-c²
    =(a²-a²-a²)+(2ab-2ab)+(b²-b²-b²)+(2ac-2ac)+(2bc-2bc)+(c²-c²-c²)
    =-a²-b²-c²
    b)(a+b+c)²+(a-b+c)²+(a+b-c)²+(-a+b+c)²
    =[(a+b)+c]²+[(a-b)+c]²+[(a+b)-c]²+[c-(a-b)]²
    =(a+b)²+2c(a+b)+c²+(a-b)²+2c(a-b)+c²+(a+b)²-2c(a+b)+c²+c²-2c(a-b)+(a-b)²
    =[(a+b)²+(a+b)²]+[2c(a+b)-2c(a+b)]+(c²+c²+c²+c²)+[(a-b)²+(a-b)²]+[2c(a-b)-2c(a-b)]
    =2(a+b)²+4c²+2(a-b²)
    =2[(a+b)²+2c²+(a-b)²]
    =2(a²+2ab+b²+2c²+a²-2ab+b²)
    =2[(a²+a²)+(2ab-2ab)+(b²+b²)+2c²]
    =2(2a²+2b²+2c²)
    =4a²+4b²+4c²

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

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