Using properties of determinants prove that - (b+c)2 a2 a2 - Maths - Determinants

Question

Using properties of determinants prove that -
(b+c)2 a2 a2
b2 (c+a)2 b2
=2abc(a+b+c)3
c2 c2 (a+b)2
In this ques i just want to know tht after applying
C1→ C1-C2,
C2→ C2-C3
in this ques how can i take (a+b+c) common from C1
and C2

Varun.Rawat · Accepted Answer

After applying the properties that is
C1 = Câ€‹1 - C3
and C2 = C2 - C3 , we get

∆ = (b+c)2-a20a20(c+a)2-b2b2c2 -(a+b)2c2 -(a+b)2(a+b)2∆
=
(a+b+c)(b+c-a)0a20(a+b+c)(c+a-b)b2(a+b+c)(c-a-b)(a+b+c)(c-a-b)(a+b)2so
we can take (a+b+c) common from C1 and C2 ∆=(a+b+c)2
(b+c-a)0a20(c+a-b)b2(c-a-b)(c-a-b)(a+b)2

Hope your doubt is cleared now
Refer the following link :

https://www meritnation
com/ask-answer/question/b-c-2-a-2-a-2-b-2-c-a-2-b-2-2abc-a-b-c-3/determinants/2386483

Using properties of determinants prove that - (b+c)2....a2........a2 b2.....(c+a)2......b2 =2abc(a+b+c)3 c2.....c2.......(a+b)2 In this ques.. i just want to know tht after applying C1→ C1-C2, C2→ C2-C3 in this ques how can i take (a+b+c) common from C1 and C2.

Using properties of determinants prove that -

(b+c)²....a²........a²

b².....(c+a)^2......b² =2abc(a+b+c)³

c².....c².......(a+b)²

In this ques.. i just want to know tht after applying C₁→ C₁-C₂, C₂→ C₂-C₃

in this ques how can i take (a+b+c) common from C₁ and C₂.