1. **State the problem:** We are given the expression $56x^4y^3 - 42x^2y^6$ and one factor $14x^2y^3$. We need to find the other factor. 2. **Formula and rule:** If $A = B \times C$, then $C = \frac{A}{B}$. Here, $A = 56x^4y^3 - 42x^2y^6$ and $B = 14x^2y^3$. We want to find $C$. 3. **Divide the expression by the given factor:** $$C = \frac{56x^4y^3 - 42x^2y^6}{14x^2y^3}$$ 4. **Split the division:** $$C = \frac{56x^4y^3}{14x^2y^3} - \frac{42x^2y^6}{14x^2y^3}$$ 5. **Simplify each term:** - For the first term: $$\frac{56}{14} = 4, \quad x^{4-2} = x^2, \quad y^{3-3} = y^0 = 1$$ So, the first term is $4x^2$. - For the second term: $$\frac{42}{14} = 3, \quad x^{2-2} = x^0 = 1, \quad y^{6-3} = y^3$$ So, the second term is $3y^3$. 6. **Write the other factor:** $$C = 4x^2 - 3y^3$$ **Final answer:** The other factor is $4x^2 - 3y^3$.