Is expansion necessary for this quadratic equation?

[Kartik.]

(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

 

[Mentallic]

(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

No, this will be a quartic (4th degree in x) whichever way you play with it. You can easily see this because the only way for it to become a quadratic is if the LHS x⁴ and x³ coefficients are cancelled, which isn't going to happen since the RHS only has a constant.

 

[pwsnafu]

(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

You should realize that 3 times 4 times 2 is equal to 24, so you definitely want to expand.