Question

Solve
$\left|\begin{array}{ccc}1& bc& a(b+c)\\ 1& ca& b(c+a)\\ 1& ab& c(a+b)\end{array}\right|$

• A. $0$
• B. $1$
• C. $abc$
• D. $ab+bc+ca$

Answer 1

The correct option is A $0$

Given

$\left|\begin{array}{ccc}1& bc& a(b+c)\\ 1& ca& b(c+a)\\ 1& ab& c(a+b)\end{array}\right|$

$=1\times (a\times c)\times (a\times c+b\times c)+b\times c\times (a\times b+b\times c)\times 1+$

$+(a\times b+a\times c)\times 1\times (a\times b)-1\times (a\times c)\times (a\times b+a\times c)-$

$-a\times b\times (a\times b+b\times c)\times 1-(a\times c+b\times c)\times 1\times (b\times c)$

$=0$