Given:
The given expression is [tex]\frac{4 d+28}{12 d+96} \cdot \frac{d^{2}+14 d+48}{d^{2}+9 d+14}[/tex]
We need to multiply the terms.
Multiplication of the terms:
Before multiplying the terms, first we shall find the factors of the quadratic equations.
Thus, we have;
[tex]\frac{4 d+28}{12 d+96} \cdot \frac{(d+6)(d+8)}{(d+2)(d+7)}[/tex]
Factor out the common terms, we get;
[tex]\frac{4 (d+7)}{12 (d+8)} \cdot \frac{(d+6)(d+8)}{(d+2)(d+7)}[/tex]
Let us cancel the common terms from the above expression.
Thus, we have;
[tex]\frac{4 }{12 } \cdot \frac{(d+6)}{(d+2)}[/tex]
Simplifying, the term, we get;
[tex]\frac{1}{3 } \cdot \frac{(d+6)}{(d+2)}[/tex]
Now, we shall multiply the terms.
Hence, multiplying the terms, we get;
[tex]\frac{(d+6)}{3(d+2)}[/tex]
Thus, the multiplied value of the given expression is [tex]\frac{(d+6)}{3(d+2)}[/tex]
