Question

(x-a)(x-b)(x+c) what will be the formula of this??​

Answer 1

(x-a)(x-b)(x-c) you should multiply the first two to get a quadratic then multiply the final factor.

(x-a)(x-b)(x-c)

= (X-C)(x^2 - (a+b)x + ab)

= x^3 - (à+b+c)x^2 + (ab+bc+ac)x + abc

notice that whatever happens to à happens to a b and c too.

(x-a)(x-b)(x-c)(x-d)

=(x-d)(x-c)(x^2 - (a+b)x + ab)

= x^4 + (a+b+c+d)x^3 + (ab + bc + bd + ac + ad +cd)x^2 + (abc + bcd + abd + acd)x + abcd

Now we notice the amount of factors is the binomial coefficient. 1 4 6 4 1 for 4 factors. For n factors it’s 1 n n(n-1)/2