Sure, let's solve the given expression step-by-step:
We start with the expression:
[tex]\[
(a - 4ax)(a + 4ax)
\][/tex]
To simplify this, we can use the difference of squares formula, which is:
[tex]\[
(A - B)(A + B) = A^2 - B^2
\][/tex]
Here, we identify [tex]\(A\)[/tex] and [tex]\(B\)[/tex] as follows:
[tex]\[
A = a \quad \text{and} \quad B = 4ax
\][/tex]
Applying the formula:
[tex]\[
(a - 4ax)(a + 4ax) = a^2 - (4ax)^2
\][/tex]
Next, we need to square the term [tex]\(4ax\)[/tex]:
[tex]\[
(4ax)^2 = (4a)^2 \cdot x^2 = 16a^2x^2
\][/tex]
Putting this back into our expression, we get:
[tex]\[
a^2 - 16a^2x^2
\][/tex]
So, the simplified form of the expression [tex]\((a - 4ax)(a + 4ax)\)[/tex] is:
[tex]\[
a^2 - 16a^2x^2
\][/tex]
Therefore, the final result is:
[tex]\[
-(16a^2x^2) + a^2 = a^2 - 16a^2x^2
\][/tex]
