1. **State the problem:** Simplify the expressions $10y \cdot 12y$ and $4y^2 \cdot 4yx^2$. 2. **Recall the multiplication rules for variables:** - When multiplying like bases, add the exponents: $a^m \cdot a^n = a^{m+n}$. - Coefficients (numbers) multiply normally. 3. **Simplify the first expression:** $$10y \cdot 12y = (10 \cdot 12)(y \cdot y) = 120y^2$$ 4. **Simplify the second expression:** $$4y^2 \cdot 4yx^2 = (4 \cdot 4)(y^2 \cdot y)(x^2) = 16y^{2+1}x^2 = 16y^3x^2$$ 5. **Final answers:** - $10y \cdot 12y = 120y^2$ - $4y^2 \cdot 4yx^2 = 16y^3x^2$