1. **State the problem:** Simplify the expression $5y^3 \cdot 32x - 4 \cdot 15x^3y^3$. 2. **Rewrite the expression clearly:** $$5y^3 \times 32x - 4 \times 15x^3y^3$$ 3. **Multiply the coefficients and variables in each term:** - First term: $5 \times 32 = 160$, variables $y^3 \times x = xy^3$ - Second term: $4 \times 15 = 60$, variables $x^3y^3$ So the expression becomes: $$160xy^3 - 60x^3y^3$$ 4. **Factor out the common terms:** Both terms have $x$ and $y^3$ in common. $$= 20xy^3(8 - 3x^2)$$ 5. **Final simplified expression:** $$20xy^3(8 - 3x^2)$$ This is the simplified form of the original expression.