Answer:
Step-by-step explanation:
[tex](\dfrac{1}{2}a-\dfrac{2}{3}b)(\dfrac{3}{5}a+\dfrac{2}{3}b)=\dfrac{1}{2}a*(\dfrac{3}{5}a+\dfrac{2}{3}b) - \dfrac{2}{3}b*(\dfrac{3}{5}a+\dfrac{2}{3}b) \\\\\\= \dfrac{1}{2}a*\dfrac{3}{5}a + (\dfrac{1}{2}a*\dfrac{2}{3}b) - \dfrac{2}{3}b*\dfrac{3}{5}a- \dfrac{2}{3}b*\dfrac{2}{3}b\\\\\\=\dfrac{3}{10}a^{2} + \dfrac{1}{3}ab - \dfrac{2}{5}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2} +\dfrac{1*5}{3*5}ab-\dfrac{2*3}{5*3}-\dfrac{4}{9}b^{2}\\\\\\[/tex]
[tex]=\dfrac{3}{10}a^{2}+\dfrac{5}{15}ab-\dfrac{6}{15}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2}-\dfrac{1}{15}-\dfrac{4}{9}b^{2}[/tex]
