The question is as followed:
Express (rootP + 2 x rootQ)(rootQ - rootP)
This is what I did:
(rootP + 2 x rootQ)(rootQ - rootP)
= rootPQ - p + 2q - 2 x rootPQ
= - rootPQ - p + 2q
Did I do this right and is this what the question was asking?
explain how you know that 5.5 is to the right of 5 1/4 on the number line
because 5.5 is larger than 5.25?
what does that have to do with the question?
Let's break down your steps and verify if you did it correctly.
The question is asking you to express the given expression: (rootP + 2 x rootQ)(rootQ - rootP). To do this, you need to expand the expression using the distributive property.
Here are the steps to expand the expression:
1) Distribute rootQ to both terms inside the first parentheses:
(rootP + 2 x rootQ)(rootQ - rootP) = rootP x rootQ - rootP x rootP + 2 x rootQ x rootQ - 2 x rootQ x rootP
2) Simplify each term:
rootP x rootQ = root(PQ)
rootP x rootP = (rootP)^2 = P
2 x rootQ x rootQ = 2 x (rootQ)^2 = 2Q
2 x rootQ x rootP = 2 x rootP x rootQ = 2 x root(PQ)
3) Combine the simplified terms:
rootP x rootQ - rootP x rootP + 2 x rootQ x rootQ - 2 x rootQ x rootP = root(PQ) - P + 2Q - 2 x root(PQ)
So, your result is:
- root(PQ) - P + 2Q - 2 x root(PQ)
Now, comparing it with your answer:
- root(PQ) - P + 2Q - 2 x root(PQ)
You have indeed computed the expression correctly and arrived at the same result. Great job!