Question

[minhhieu]

(a+b+c)²+(a-b+c)²-2.(b-c)²

giải dùm mình nha

Answer 1

[Ngô Chi Lan]

Thu gọn-.-?

Ta có: \(\left(a+b+c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)

\(=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2+2\left(ca-ab-bc\right)-2\left(b^2-2bc+c^2\right)\)

\(=2a^2+2b^2+2c^2+4ca-2b^2+4bc-2c^2\)

\(=2a^2+4ca+4bc\)

Answer 2

[l҉o҉n҉g҉ d҉z҉]

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

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

= [ ( a + b )² + 2( a + b )c + c² ] + [ ( a - b )² + 2( a - b )c + c² ] - 2( b² - 2bc + c² )

= [ a² + 2ab + b² + 2ac + 2bc + c² ] + [ a² - 2ab + b² + 2ac - 2bc + c² ] - 2b² + 4bc - 2c²

= a² + 2ab + b² + 2ac + 2bc + c² + a² - 2ab + b² + 2ac - 2bc + c² - 2b² + 4bc - 2c²

= 2a² + 4bc + 4ac

= 2( a² + 2bc + 2ac )