Toán Lớp 8: $(a-b+c)^{2}-(c-b)^{2}+2(a-b+c)$ $(b-c)$ [Tính_nhanh]

TRẢ LỜI

1. (a-b+c)^2 – (c-b)^2 + 2(a-b+c)(b-c)

   = (a-b+c)^2 + (b-c)^2 + 2(a-b+c)(b-c)

   = (a-b+c)^2 + 2(a-b+c)(b-c) + (b-c)^2

   = [(a-b+c) + (b-c)]^2

   = (a – b + c + b -c)^2

   = a^2

   Trả lời
2. Chú ý:

   $(A-B)^2=(-B-A)^2=(B-A)^2$

   $(A+B)^2=A^2+2AB+B^2$

   Bài làm:

   $(a-b+c)^2-(c-b)^2+2(a-b+c)(b-c)$

   $= (a-b+c)^2+(b-c)^2+2(a-b+c)(b-c)$

   $= (a-b+c)^2+2(a-b+c)(b-c)+(b-c)^2$

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

   $= a^2$

   Trả lời