Question

CMR

ab.(a+b)-bc.(b+c)+ac.(a-c)=(a+b).(b+c).(a-c)

Answer 1

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

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

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

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

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

\(\Rightarrowđpcm\)