Let's simplify the given expression step by step:
Starting with the expression:
[tex]\[ y^3 + 4x \left( 6y^3 + 3x \right) \][/tex]
1. Distribute the multiplication within the parentheses:
[tex]\[ y^3 + 4x \cdot 6y^3 + 4x \cdot 3x \][/tex]
2. Perform the multiplications:
[tex]\[ y^3 + 24xy^3 + 12x^2 \][/tex]
3. Rearrange the terms (usually in decreasing order of the powers):
[tex]\[ 12x^2 + 24xy^3 + y^3 \][/tex]
So, the simplified expression is:
[tex]\[ 12x^2 + 24xy^3 + y^3 \][/tex]
This is the expanded and simplified form of the given expression.
