Answer:
Given the following:
\(X = r+2\)
\(Y = 2r -9\) and
\(Z = r^2+17r+30\)
Simplify: \([X.Y-Z] \div X\)
First simplify: \(X \cdot Y\)
\(X \cdot Y = (r+2) \cdot (2r-9) = r(2r-9)+2(2r-9)\)
The distributive property says that:
\(a \cdot (b+c) = a\cdot b+ a\cdot c\)
\(r(2r-9)+2(2r-9) = 2r^2-9r+4r-18 = 2r^2-5r-18\)
∴\(X \cdot Y=2r^2-5r-18\)
\(X\cdot Y -Z = 2r^2-5r-18 -(r^2+17r+30) =2r^2-5r-18 -r^2-17r- 30\)
Combine like terms;
\(X\cdot Y -Z =r^2-22r-48=r^2-24r+2r-48 = r(r-24)+2(r-24) = (r+2)(r-24)\)
Then;
\(\frac{X \cdot Y -Z}{X} = \frac{ (r+2)(r-24)}{r+2} = r-24\)
Therefore, the simplified form of \([X.Y-Z] \div X\) is r- 24
