The question was:
x (3x2 - 2x + 5)
My working out+answer:
=3x2 - 2x2 + 5
=x2 + 5
Textbook answer:
=3x3 - 2x2 + 5
Now I understand how they got that answer. When I multiply x with 3x^2, the exponent changes from 3x^2 ---> 3x^3.
But then doesn't that conflict with one of the indices laws?:
(am)x = am × x
So applying that rule:
▪x is to the power of 1 (since anything to the power of 1 is itself)
▪3x^2 is to the power of 2
• so it would be 3x2×1
• that's how I got 3x3
Why does it not work?
x * x^2 = x^(2+1) = x^3
this is NOT (x^m)^n this is x^m * x^n = x^(m+n)
so x^1 * x^2 = x^(2+1) = x^3
x * x^2 = x^(2+1) = x^3
this is NOT (x^m)^n this is x^m * x^n = x^(m+n)
so x^1 * x^2 = x^(2+1) = x^3