Show that:

(3x-1)(x+5)(4x-3) = 12x^3 + 47x^2 - 62x +15

for all values of x.

(3x-1)(x+5)(4x-3) = (?????)(4x-3)

Expand into 6 terms: ????????

Simplify: ????????

Thank you.

3 answers

just expand the left side. It will be the same as the right side. One way to start would be

(3x-1)(x+5)(4x-3)
= 3x(x+5)(4x-3)-(x+5)(4x-3)

Now, (x+5)(4x-3)=4x^2+17x-15 so you can proceed with

= 3x(4x^2+17x-15)-(4x^2+17x-15)
= ...
I'm confused
The question that teacher has asked is that show that (3x-1)(x+5)(4x-3)=12x^3+47x^2-62x+15 for all values of x