Simplify `(a+b+c)(a+b-c)`

Simplify (a+b)(c-d)+(a-b)(c-d)+2(ac+bd)

If a ne 6, b , c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 , then abc =

In a triangle ABC, if /_B=60^(@) , then the expression (a+b+c)(a-b+c) is

Show that the points P(a+2b+c),Q(a-b-c),R(3a+b+2c) and S(5a+3b+5c) are coplanar given that a,b and c are non-coplanar.

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

The value of determinant |(a-b ,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is

The expression ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2 c^2) for a triangle ABC is equal to

If (a+b)/(1-a b), b, (b+c)/(1-b c) are in A.P, then a, (1)/(b), c are in

Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c, a+ b) are collinear.

Using determinants show that points A(a, b + c), B(b, c + a) and C(c, a + b) are collinear.