Here are the simplified expressions: l) Step 1: Use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a=7a^2$ and $b=b^5$. $$ (7a^2 - b^5)^2 = (7a^2)^2 - 2(7a^2)(b^5) + (b^5)^2 $$ Step 2: Simplify the terms. $$ = 49a^4 - 14a^2b^5 + b^{10} $$ The simplified expression is $\boxed{49a^4 - 14a^2b^5 + b^{10}}$. m) Step 1: Use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a=\frac{x}{2}$ and $b=1$. $$ \left(\frac{x}{2} - 1\right)^2 = \left(\frac{x}{2}\right)^2 - 2\left(\frac{x}{2}\right)(1) + 1^2 $$ Step 2: Simplify the terms. $$ = \frac{x^2}{4} - x + 1 $$ The simplified expression is $\boxed{\frac{x^2}{4} - x + 1}$. n) Step 1: Use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a=\frac{x}{2}$ and $b=3$. $$ \left(\frac{x}{2} - 3\right)^2 = \left(\frac{x}{2}\right)^2 - 2\left(\frac{x}{2}\right)(3) + 3^2 $$ Step 2: Simplify the terms. $$ = \frac{x^2}{4} - 3x + 9 $$ The simplified expression is $\boxed{\frac{x^2}{4} - 3x + 9}$. o) Step 1: Use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a=\frac{y}{5}$ and $b=1$. $$ \left(\frac{y}{5} - 1\right)^2 = \left(\frac{y}{5}\right)^2 - 2\left(\frac{y}{5}\right)(1) + 1^2 $$ Step 2: Simplify the terms. $$ = \frac{y^2}{25} - \frac{2y}{5} + 1 $$ The simplified expression is $\boxed{\frac{y^2}{25} - \frac{2y}{5} + 1}$. 3 done, 2 left today. You're making progress.