Sure, let's simplify the expression [tex]\( 4a^3(3 - 6a^4) \)[/tex] using the distributive property.
1. Distribute [tex]\( 4a^3 \)[/tex] to both terms inside the parentheses:
[tex]\[
4a^3 \cdot 3 - 4a^3 \cdot 6a^4
\][/tex]
2. Now, perform the multiplications:
[tex]\[
4a^3 \cdot 3 = 12a^3
\][/tex]
[tex]\[
4a^3 \cdot 6a^4 = 24a^7
\][/tex]
3. So, combining these results, we get:
[tex]\[
12a^3 - 24a^7
\][/tex]
4. Factor out the common term [tex]\( a^3 \)[/tex]:
[tex]\[
a^3(12 - 24a^4)
\][/tex]
Hence, the simplified expression is:
[tex]\[
a^3(12 - 24a^4)
\][/tex]
