ab+ca2bc+ab2ca+bc2 c2→c1+c2 a+b+c 1b+ca21c+ab21a+bc2 (a+b+c) 1b+ca20a-bb2-a20a-cc2-a2 R2→R2-R1, R3→R3-R1(a+b+c) (a-b) (c-a) 1b+ca201-(a+b)0-1c+a R3→R3+R2 (a+b+c) (a-b) (c-a) 1b+ca201-(a+b)00c-b ∴ -(a-b) (b-c) (c-a) (a+b+c)

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$|\begin{matrix} a & b + c & a^{2} \\ b & c + a & b^{2} \\ c & a + b & c^{2} \end{matrix}| =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(a-b) (b-c) (c-a)

-(a-b)(b-c)(c-a) (a+b+c)

abc(a-b) (b-c) (c-a)

2(a-b) (b-c) (c-a)

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{rcl} |\begin{matrix} a & b + c & a^{2} \\ b & c + a & b^{2} \\ c & a + b & c^{2} \end{matrix}| \\ c_{2} & \to & c_{1} + c_{2} \\ (a + b + c) |\begin{matrix} 1 & b + c & a^{2} \\ 1 & c + a & b^{2} \\ 1 & a + b & c^{2} \end{matrix}| \\ (a + b + c) |\begin{matrix} 1 & b + c & a^{2} \\ 0 & a - b & b^{2} - a^{2} \\ 0 & a - c & c^{2} - a^{2} \end{matrix}| (R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}) \end{array}$

$(a + b + c) (a - b) (c - a) |\begin{matrix} 1 & b + c & a^{2} \\ 0 & 1 & - (a + b) \\ 0 & - 1 & c + a \end{matrix}| R_{3} \to R_{3} + R_{2} (a + b + c) (a - b) (c - a) |\begin{matrix} 1 & b + c & a^{2} \\ 0 & 1 & - (a + b) \\ 0 & 0 & c - b \end{matrix}| ∴ - (a - b) (b - c) (c - a) (a + b + c)$