Question

Prove that for any value of x the expression (x-3)(x+7)-(x+5)(x-1) is negative

Answer 1

you can prove it by making the first 2 expression less than the last 2 expressions

Explanation:

(x-3)(x+7)-(x+5)(x-1)

(x-3)(x+7) < (x+5)(x-1)

x^2 +4x-21 < x^2 +4x-5

• cancel out some terms

then it become -21<-5 which is true