e. \( (2 a+5)^{2} \)

To find the expansion of \( (2a + 5)^2 \), you can use the formula for the square of a binomial, which is \( (x + y)^2 = x^2 + 2xy + y^2 \). Here, \( x = 2a \) and \( y = 5 \). So, we start with squaring \( x \), \( 2xy \), and squaring \( y \): \((2a)^2 + 2(2a)(5) + 5^2 = 4a^2 + 20a + 25\). So, the expanded form is \( 4a^2 + 20a + 25 \). If you’ve ever baked a cake, think of expanding a binomial like mixing ingredients: you start with two main flavors (just like your \( 2a \) and \( 5 \)) and combine them in different ways to create a delicious treat! Each term in your expansion represents a unique flavor that's critical to the overall taste. To avoid mistakes when expanding, double-check each step! A common slip is forgetting to square all parts fully—remember, both \( x \) and \( y \) must be squared, and don't overlook the cross-terms! A handy tip is to write out each step clearly; visualizing it can help you catch those pesky errors before they sneak into your final result!