Video Transcript
If 𝑥 is equal to three root three and 𝑦 is equal to five, evaluate 𝑥 squared minus 𝑦 squared all cubed.
In this question, we are given values of 𝑥 and 𝑦 and asked to evaluate an expression involving 𝑥 and 𝑦. We will do this by substituting the given values into the expression. Remember, we want to evaluate the expression inside the parentheses first.
We obtain three root three squared minus five squared all cubed. To evaluate this expression, we note that we want to start by evaluating the squares. There are many ways of doing this. One way is to recall that 𝑎𝑏 all squared is equal to 𝑎 squared 𝑏 squared. This then allows us to write three root three squared as three squared times root three squared. We can then calculate that five squared is 25 to get three squared times root three squared minus 25 all cubed.
We can then recall that squaring the square root of a nonnegative number leaves it unchanged. So, root three squared is three. We then multiply this by three squared to get 27. Hence, our expression simplifies to give 27 minus 25 all cubed. We can then evaluate that 27 minus 25 is two. So, we are left with two cubed. Finally, we can evaluate that two cubed is equal to eight.
Hence, if 𝑥 is equal to three root three and 𝑦 is equal to five, then 𝑥 squared minus 𝑦 squared all cubed is equal to eight.
