Question 615587
{{{45x^3-15x^2}}}
When factoring, always start with the greatest common factor, GCF, if it is not a 1. The GCF here is {{{15x^2}}}:
{{{15x^2(3x-1)}}}
Since the second factor above will not factor any further we are finished.<br>
{{{z^2-225}}}
The GCF here is 1 and we almost never factor out a 1. So we proceed to other methods of factoring. I prefer to try the factoring patterns after the GCF.<br>
Your expression has just two terms. There are three factoring patterns for two-term expressions. They are known as "sum of cubes", "difference of cubes" and "difference of squares". Since {{{z^2}}} is not a perfect cube we cannot use either of the "cubes" patterns. {{{z^2}}} is obviously a perfect square and we definitely have a difference. But is 225 a perfect square? Even if you do not immediately know whether 225 is a perfect square, you should be able, with just a little effort, to figure out that 225 <i>is</i> a perfect square! {{{225 = 15^2}}}. So we do have a difference of squares and we can use that pattern, {{{a^2-b^2 = (a+b)(a-b)}}}, to factor your expression:
(z+15)(z-15)
Ans since neither factor will factor further we are finished.