To factorize the expression [tex]\(16a - 4a^2\)[/tex] fully, let's go through it step by step.
1. Identify Common Factors:
The first step is to identify any common factors in the terms of the expression [tex]\(16a - 4a^2\)[/tex]. Both terms [tex]\(16a\)[/tex] and [tex]\(-4a^2\)[/tex] share a common factor of [tex]\(4a\)[/tex].
2. Factor Out the Common Factor:
Once we identify the common factor, we can factor it out of each term:
[tex]\[
16a - 4a^2 = 4a(4) - 4a(a)
\][/tex]
3. Simplify Within Parentheses:
Now, we simplify the expression inside the parentheses:
[tex]\[
4a(4 - a)
\][/tex]
4. Consider the Sign:
After factoring out the common factor, observe if there is any common factor that can be further factored out. In this expression, [tex]\(4a(4 - a)\)[/tex] is already fully factored. However, to get a correct and simpler factorized form, we note that:
[tex]\[
4a(4 - a) = -4a(a - 4)
\][/tex]
Since [tex]\(4a\)[/tex] and [tex]\(-4a\)[/tex] are multiples, the correct factorized form simplifies the expression neatly.
Therefore, the fully factorized form of [tex]\(16a - 4a^2\)[/tex] is:
[tex]\[
-4a(a - 4)
\][/tex]
