If | array cc x^3+2 x^2+3 x-2 & x^2+2 x+4 x^3-x^2-2 x-1 & 3 x^3-2 x^2+4 x-2 array |=a x^6+b x^5+c x^4+d x^3+e x^2+f x+g , then a+b+c+d+e+f is equal to

Step-by-step solution

Given, | array cc x^3+2 x^2+3 x-2 & x^2+2 x+4 x^3-x^2-2 x-1 & 3 x^3-x^2+4 x-2 array |=a x^6+b x^5+c x^4+d x^3+e x^2+f x+g On expanding the determinant, aligned (x^3+2 x^2+3 x-2 ) & (3 x^3-2 x^2+4 x-2 ) & - (x^2+2 x+4 ) (x^3-x^2-2 x-1 ) aligned aligned 3 x^6-2 x^5 & +4 x^4-2 x^3+6 x^5-4 x^4+8 x^3 & -4 x^2+9 x^4-6 x^3+12 x^2 & -6 x-6 x^3+4 x^2-8 x+4 & - x^5-x^4-2 x^3-x^2+2 x^4 . & .-2 x^3-4 x^2-2 x+4 x^3-4 x^2-8 x-4 aligned aligned 3 x^6+4 x^5 & +9 x^4-6 x^3+12 x^2 & -14 x+4-x^5-x^4+9 x^2+10 x+4 aligned 3 x^6+3 x^5+8