Question

( a-b-c)² - (a-b+c)² = ? 

Answer 1

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

\(=\left(a-b-c+a-b+c\right)\left(a-b-c-a+b-c\right)\)

\(=\left(2a-2b\right)\left(-2c\right)\)

\(=-4ac+4bc\)

Answer 2

Áp dụng hằng đăngr thức \(a^2-b^2=\left(a+b\right)\left(a-b\right)\)

Ta có

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

\(=\left(a-b-c+a-b+c\right)\left(a-b-c-a+b-c\right)=\left(2a-2b\right)\left(-2c\right)=-4\left(ca-cb\right)\)

Answer 3

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

\(=-2c\left(2a-2b\right)\)
\(=-4c\left(a-b\right)\)