Question

Chứng minh:
( a + c) ( a - c) - b( 2a - b ) - ( a - b + c ) (a - b - c ) = 0

Answer 1

Ta có:

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

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

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

\(=a^2-c^2-2ab+b^2-a^2+2ab-b^2+c^2=0=VP\)

Vậy \(\left(a+c\right)\left(a-c\right)-b\left(2a-b\right)-\left(a-b+c\right)\left(a-b-c\right)=0\)(đpcm)

Chúc bạn học tốt!!!

Answer 2

Ta có:

\(\text{( a + c) ( a - c) - b( 2a - b ) - ( a - b + c ) (a - b - c )}\)

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

=\(a^2-c^2-2ab+b^2-a^2+2ab-b^2+c^2\)=0

Do đó ( a + c) ( a - c) - b( 2a - b ) - ( a - b + c ) (a - b - c ) = 0 (đpcm)