Today's soundtrack is Rag'n'Bone Man: Human, a cool hipster neo-soul album that my friend Richard introduced me to. It's great music with gorgeous, passionate vocals.
This afternoon, I'm continuing to work on the assignment portion of the lesson about multiplying and dividing radicals. This part of the lesson covers multiplying radicals with variables, which requires identifying the value of which each variable is defined before using distributive properties to multiply the expression.
One really interesting thing that I have found through a fair bit of trial and error is that a negative expression inside of parentheses only inverts the first set of the expression if there is a square outside of the parentheses - eg, -(√a - 3√b)² is expressed as (-√a + 3√b) (√a - 3√b), which equals -√a² + 3√ab + 3√ab - 9√b², which we then simplify to -a + 6√ab - 9b.
