Set 6: Quadratic Equations

Choice D is correct. Choice D is the correct answer. To expand a binomial squared $(a - b)^2$, use the formula $a^2 - 2 ab + b^2$. 1. Here $a = 2 x$ and $b = 5$. 2. $a^2 = (2 x)^2 = 4 x^2$. 3. $-2 ab = -2(2 x)(5) = -20 x$. 4. $b^2 = 5^2 = 25$. Combine them: $4x^2 - 20 x + 25$. Choice A is incorrect because it misses the middle term. This is a very common mistake. Choice B is incorrect because it also misses the middle term. Choice C is incorrect because the middle term is calculated as $-2(x)(5)$ instead of $-2(2 x)(5)$.