College

Select the expressions that are equivalent to [tex]$7f + 9f$[/tex].

A. [tex]$16f$[/tex]

B. [tex][tex]$17f$[/tex][/tex]

C. [tex]$f + 16$[/tex]

D. [tex]$f \cdot 16$[/tex]

Answer :

To find an expression equivalent to
[tex]$$7f + 9f,$$[/tex]
we begin by noticing that both terms have the same variable [tex]$f$[/tex]. This means we can combine the coefficients of [tex]$f$[/tex].

1. Write the expression with the coefficients:
[tex]$$7f + 9f.$$[/tex]

2. Factor out the common variable [tex]$f$[/tex]:
[tex]$$f(7 + 9).$$[/tex]

3. Add the coefficients:
[tex]$$7 + 9 = 16.$$[/tex]

4. Multiply the common factor back:
[tex]$$f \cdot 16 = 16f.$$[/tex]

Thus,
[tex]$$7f + 9f = 16f.$$[/tex]

Among the provided options, the expression equivalent to [tex]$7f + 9f$[/tex] is:

[tex]$$\boxed{16f}.$$[/tex]