Question

Rút gọn biểu thức:

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

Answer 1

C = (a + b - c)² - (a - c)² - 2a + 2bc

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

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

Answer 2

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

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

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

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

\(=b^2\)

Vậy \(C=b^2\)

Answer 3

\(C=\left(a+b-c\right)^2-\left(a-c\right)^2-2a+2bc\\ =\left(a+b\right)^2-2\left(a+b\right)c+c^2-\left(a^2-2ac+c^2\right)-2a+2bc\\ =\left(a^2+2ab+b^{^2}\right)-2ac-2bc+c^2-a^2+2ac-c^2-2a+2bc\\ =2ab+b^2=b\left(2a+b\right)\)