PTĐTTNT DẠNG ĐỐI XỨNG VÒNG QUANH 1,(b+c)(c+a)(b-a)+(b+c)(a+b)(a-c)+(a-b)(b-c)(a-c)

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1. 1,$(b+c)(c+a)(b-a)+(b+c)(a+b)(a-c)+(a-b)(b-c)(a-c)$

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

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

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

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

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

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

   $=(b-c)[(b+c).2a+(a-b)(a-c)]$

   $=(b-c)(2ab+2ac+a^2-ab-ca+bc)$

   $=(b-c)(a^2+ab+ac+bc)$

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

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

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2. Đáp án:

    

   Giải thích các bước giải:

   (b+c)(c+a)(b−a)+(b+c)(a+b)(a−c)+(a−b)(b−c)(a−c)(b+c)(c+a)(b−a)+(b+c)(a+b)(a−c)+(a−b)(b−c)(a−c)

   =(b+c)(c+a)(b−a)+(b+c)(a+b)(a−b+b−c)+(a−b)(b−c)(a−c)=(b+c)(c+a)(b−a)+(b+c)(a+b)(a−b+b−c)+(a−b)(b−c)(a−c)

   =(b+c)(c+a)(b−a)+(b+c)(a+b)(a−b)+(b+c)(a+b)(b−c)+(a−b)(b−c)(a−c)=(b+c)(c+a)(b−a)+(b+c)(a+b)(a−b)+(b+c)(a+b)(b−c)+(a−b)(b−c)(a−c)

   =(b+c)(a−b)(a+b−c−a)+(b−c)[(b+c)(a+b)+(a−b)(a−c)]=(b+c)(a−b)(a+b−c−a)+(b−c)[(b+c)(a+b)+(a−b)(a−c)]

   =(b+c)(a−b)(b−c)+(b−c)[(b+c)(a+b)+(a−b)(a−c)]=(b+c)(a−b)(b−c)+(b−c)[(b+c)(a+b)+(a−b)(a−c)]

   =(b−c)[(b+c)(a−b)+(b+c)(a+b)+(a−b)(a−c)]=(b−c)[(b+c)(a−b)+(b+c)(a+b)+(a−b)(a−c)]

   =(b−c)[(b+c)(a−b+a+b)+(a−b)(a−c)]=(b−c)[(b+c)(a−b+a+b)+(a−b)(a−c)]

   =(b−c)[(b+c).2a+(a−b)(a−c)]=(b−c)[(b+c).2a+(a−b)(a−c)]

   =(b−c)(2ab+2ac+a2−ab−ca+bc)=(b−c)(2ab+2ac+a2−ab−ca+bc)

   =(b−c)(a2+ab+ac+bc)=(b−c)(a2+ab+ac+bc)

   =(b−c)[a(a+b)+c(a+b)]=(b−c)[a(a+b)+c(a+b)]

   =(b−c)(a+b)(a+c)

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