Certainly! Let's factor the expression [tex]\(12 w^2 - 12 u^2\)[/tex].
1. Identify the common factor:
First, we observe that both terms in the expression [tex]\(12 w^2 - 12 u^2\)[/tex] have a common factor of 12. We can factor 12 out of the expression:
[tex]\[
12 w^2 - 12 u^2 = 12(w^2 - u^2)
\][/tex]
2. Recognize the difference of squares:
Inside the parentheses, we have [tex]\(w^2 - u^2\)[/tex], which is a difference of squares. The difference of squares can be factored using the identity [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex]. Here, [tex]\(a = w\)[/tex] and [tex]\(b = u\)[/tex].
[tex]\[
w^2 - u^2 = (w - u)(w + u)
\][/tex]
3. Combine the factored parts:
Now we substitute back into the expression where we factored out the 12:
[tex]\[
12(w^2 - u^2) = 12(w - u)(w + u)
\][/tex]
4. Include a negative sign correctly if necessary:
If there are specific requirements of arranging terms or considering the factorization signs, ensure the expressions fulfill standard mathematical conventions. In this context, we jointly factor -12 to emphasize factor symmetry:
[tex]\[
-12(u - w)(u + w)
\][/tex]
Hence, the completely factored form of the expression [tex]\(12 w^2 - 12 u^2\)[/tex] is:
[tex]\[
-12(u - w)(u + w)
\][/tex]
