Question

How do you factor `3n ^ { 2} - 60n + 300` completely?

Answer 1

`3n^2-60n+300 = 3(n-10)^2`

Explanation:

Note that in general:

`(a+b)^2 = a^2+2ab+b^2`

and:

`(a-b)^2 = a^2-2ab+b^2`

In our example, once we have separated out the common factor `3`, we can see that the remaining quadratic trinomial has this form:

`3n^2-60n+300 = 3(n^2-20n+100)`

`color(white)(3n^2-60n+300) = 3(n^2-2(n)(10)+10^2)`

`color(white)(3n^2-60n+300) = 3(n-10)^2`