Question

Using properties of determinant show that
|a+b a b|
| a a+c c |=4abc
| b c b+c|​

Answer 1

Answer:

4abc

Step-by-step explanation:

a+b       a            b

a           a+c        c

b           c            b+c

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

= (a + b) ( ab + ac + bc + c² - c²) - a(ab + ac - bc) + b(ac - ab - bc)

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

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

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

= a( 2bc) + b(2ac)

= 2abc + 2abc

= 4abc

Answer 2

Answer:

This Answer is confirmed I can note it