Simplify `(ab+bc)^2-2ab^2c`

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 in x are equal, show that either a=0 or a^(3)+b^(3)+c^(3)=3abc .

If a^2+b^2+c^2=0 and |(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)|=ka^2b^2c^2 , then the value of k is :

Subtract: 5a^2-7ab+5b^2 from 3ab-2a^2-2b^2

The determinant |(b^2-ab,b-c,-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2)| equals :

If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=lamdaa^2b^2c^2 then the value of lamda is :

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

Prove that |(1,a^2,bc),(a,b^2,ca),(1,c^2,ab)|=(a-b)(b-c)(c-a)

Simplify combining like terms: 3a-2b-ab-(a-b+ab)+3ab+b-a

Find the proudct (a-b-c) (a ^(2) + b ^(2) + c ^(2) - ab + bc-ca) without actual multiplication.