Sure, let's expand the expression [tex]\((1 - 3ax)(1 + 3ax)\)[/tex].
1. First, apply the distributive property (also known as FOIL in binomials):
[tex]\[
(1 - 3ax)(1 + 3ax) = 1 \cdot 1 + 1 \cdot (3ax) + (-3ax) \cdot 1 + (-3ax) \cdot (3ax)
\][/tex]
2. Now, multiply each pair of terms:
[tex]\[
1 \cdot 1 = 1
\][/tex]
[tex]\[
1 \cdot (3ax) = 3ax
\][/tex]
[tex]\[
(-3ax) \cdot 1 = -3ax
\][/tex]
[tex]\[
(-3ax) \cdot (3ax) = -9a^2x^2
\][/tex]
3. Combine all the terms:
[tex]\[
1 + 3ax - 3ax - 9a^2x^2
\][/tex]
4. Notice that the middle terms [tex]\(3ax\)[/tex] and [tex]\(-3ax\)[/tex] cancel each other out:
[tex]\[
1 - 9a^2x^2
\][/tex]
Therefore, the expanded form of [tex]\((1 - 3ax)(1 + 3ax)\)[/tex] is:
[tex]\[
1 - 9a^2x^2
\][/tex]
Thus, the final expression is:
[tex]\[
-9a^2x^2 + 1
\][/tex]
