f. \( (-26 a+10 b)(-3 a-5 b)= \) g. \( \left(\frac{3}{5} X^{3} y+\frac{6}{9} x^{2} y^{3}-\frac{1}{11} X Y^{4} Z\right)\left(-\frac{2}{3} x^{2} y\right)= \) h. \( \left(-15 x^{m+3} y^{2}\right)\left(-3 x^{m+2}+2 x^{m} y-5 x y^{2}\right)= \) 1. \( \left(-2 n^{3}+14 n\right)\left(-8 n^{3}-3+6 n\right)= \) j. \( \left(7 b^{3}-12 b-9\right)\left(-6 b^{2}+8 b-3\right)= \)

Let's solve each of the expressions step by step. ### f. \( (-26 a + 10 b)(-3 a - 5 b) \) Using the distributive property (FOIL method): \[ (-26 a)(-3 a) + (-26 a)(-5 b) + (10 b)(-3 a) + (10 b)(-5 b) \] Calculating each term: 1. \( (-26 a)(-3 a) = 78 a^2 \) 2. \( (-26 a)(-5 b) = 130 ab \) 3. \( (10 b)(-3 a) = -30 ab \) 4. \( (10 b)(-5 b) = -50 b^2 \) Now combine like terms: \[ 78 a^2 + (130 ab - 30 ab) - 50 b^2 = 78 a^2 + 100 ab - 50 b^2 \] So, the result is: \[ \boxed{78 a^2 + 100 ab - 50 b^2} \] ### g. \( \left(\frac{3}{5} x^{3} y + \frac{6}{9} x^{2} y^{3} - \frac{1}{11} x y^{4} z\right)\left(-\frac{2}{3} x^{2} y\right) \) Distributing \( -\frac{2}{3} x^{2} y \): \[ \left(\frac{3}{5} x^{3} y\right)\left(-\frac{2}{3} x^{2} y\right) + \left(\frac{6}{9} x^{2} y^{3}\right)\left(-\frac{2}{3} x^{2} y\right) + \left(-\frac{1}{11} x y^{4} z\right)\left(-\frac{2}{3} x^{2} y\right) \] Calculating each term: 1. \( \left(\frac{3}{5} x^{3} y\right)\left(-\frac{2}{3} x^{2} y\right) = -\frac{2}{5} x^{5} y^{2} \) 2. \( \left(\frac{6}{9} x^{2} y^{3}\right)\left(-\frac{2}{3} x^{2} y\right) = -\frac{4}{9} x^{4} y^{4} \) 3. \( \left(-\frac{1}{11} x y^{4} z\right)\left(-\frac{2}{3} x^{2} y\right) = \frac{2}{33} x^{3} y^{5} z \) Combining these gives: \[ -\frac{2}{5} x^{5} y^{2} - \frac{4}{9} x^{4} y^{4} + \frac{2}{33} x^{3} y^{5} z \] So, the result is: \[ \boxed{-\frac{2}{5} x^{5} y^{2} - \frac{4}{9} x^{4} y^{4} + \frac{2}{33} x^{3} y^{5} z} \] ### h. \( \left(-15 x^{m+3} y^{2}\right)\left(-3 x^{m+2} + 2 x^{m} y - 5 x y^{2}\right) \) Distributing \( -15 x^{m+3} y^{2} \): \[ (-15 x^{m+3} y^{2})(-3 x^{m+2}) + (-15 x^{m+3} y^{2})(2 x^{m} y) + (-15 x^{m+3} y^{2})(-5 x y^{2}) \] Calculating each term: 1. \( (-15 x^{m+3} y^{2})(-3 x^{m+2}) = 45 x^{2m+5} y^{2} \) 2. \( (-15 x^{m+3} y^{2})(2 x^{m} y) = -30 x^{2m+3} y^{3} \) 3. \( (-15 x^{m+3} y^{2})(-5 x y^{2}) = 75 x^{2m+4} y^{4} \) Combining these gives: \[ 45 x^{2m+5} y^{2} - 30