Toán Lớp 8: `Tính:` `[(a+b)-c]^2` `(a-b+c)^2` `(a-b-c)^2`

Question

Toán Lớp 8:  Tính: [(a+b)-c]^2 (a-b+c)^2 (a-b-c)^2

dinhcongson · Answer

[(a+b)&minus;c]&sup2;   =a&sup2;+b&sup2;+c&sup2;+2ab&minus;2ac&minus;2bc   (a - b + c)&sup2;   =a&sup2;+b&sup2;+c&sup2;&minus;2ab&minus;2ab+2ca    (a &ndash; b &ndash; c)&sup2;    = [(a &ndash; b) &ndash; c]&sup2;     = (a &ndash; b)&sup2;&ndash; 2(a &ndash; b)c + c&sup2;     = a&sup2;&ndash; 2ab + b&sup2; &ndash; 2ac + 2bc + c&sup2;     = a&sup2; + b&sup2; + c&sup2;&ndash; 2ab + 2bc &ndash; 2ac.

myngocla · Answer

$a)[(a+b)-c]^{2}$   $=(a+b)^{2}-2c(a+b)+c^2$   $=a^2+b^2+c^2{}+2ab-2ac-2bc$   $b)(a-b+c)^{2}$   $=(a-b)^{2}+2c(a-b)+c^2$   $=a^{2}+b^2+c^2-2ab-2ab+2ac$   $c)(a-b-c)^{2}$   $=(a-b)^{2}-2c(a-b)+c^2$   $=a^{2}+b^2+c^2-2ab+2bc-2ca$   &Aacute;p dụng HĐT số 1 v&agrave; 2:   $A^{2}+2AB+B^2=(A+B)^2$   $A^{2}-2AB+B^2=(A-B)^2$   Ch&uacute;c bạn học tốt !!!!!