Evaluate : (ix) `(a+ bc ) (a- bc) (a^2 + b^2 c^2)`

Evaluate : (vi) (a + bc ) ( a- bc ) (a^2 + b^2 c^2)

If a= 2, b= 3 and c= 4, find the value of : (ab + bc + ca- a^(2) -b^(2)-c^(2))/(3abc-a^(3)-b^(3)-c^(3)) , using suitable identity

If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2 , then k is equal to

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|

If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

Factorise : b^(2) + c^(2) + 2bc - a^(2)

If a + b+ c= p and ab + bc + ca= q , find a^(2) +b^(2) + c^(2)

Prove that: |-a^2 ab ac ba -b^2 bc ac bc c^2| =4a^2b^2c^2 .

Factorise : a^(2) - b^(2) - c^(2) +2bc