What is the answer to f(10)= 5(x-1)(2x+3)

 " 1035 " .

       →    "  F(10) = 1035 " .

Step-by-step explanation:

To solve:

For the "right-hand side" of the equation;  substitute "10" for all "x" values:

Given:  

       F(10) = 5(x - 1)(2x + 3) ;

  →   F(10) = 5(10-1)(2*10 + 3) ;

How, to simplify the right-hand side of the equation;

 Solve using PE MD AS ; the mnemonic device for the order of operations to use for simplifying an expression:

  Please Excuse My Dear Aunt Sally [or: Susan—either name is fine] :

or the variant:

  Be Excused,  My Dear Aunt Sally/Susan .

in which the letters of the first words of the sentence in this mnemonic device represent the order of operations performed, as follows:

 (Parentheses, followed by Exponents);  if these occur; in that order;

   or:  using the variant:

  {Brackets, followed by Exponents};  if these occur, in that order;

     — in which "Parentheses" are considered a type of "Brackets" ;

         — and in which if both :  Brackets  and  Parentheses occur,

                 the "Brackets", take first in the order of operations

                 [if they occur];   followed by:  "Parentheses" ;

                  and then followed by:  "Exponents" (if they occur);

then:  Multiplication (if it occurs) and Division (if it occurs);

However,  instead of "Multiplication followed by Division" ;

  the difference is that these operations are performed from left to right— as they appear (if both Multiplication and Division occur) within the expression ;

then:  Addition (if it occurs) and Subtraction (if it occurs);

However,  instead of "Addition followed by Subtraction" ;

  the difference is that these operations are performed from left to right— as they appear (if both Addition and Subtraction occur) within the expression.

So:

  Given:  

       F(10) = 5(x - 1)(2x + 3) ;

  →   F(10) = 5(10-1)(2*10 + 3) ;

We can calculate—and simplify—the "right-hand side" of the equation; as follows:

We have:  

  →   " 5(10-1)(2*10 + 3) " ;

  →   that is;  " 5 * (10 - 1) * (2*10 + 3) ;

We do have "parentheses" in this expression:

We shall begin by simplifying the values within the two (2) terms that are enclosed within parentheses:

Start with:  

" (10 - 1) " ;  

  10 - 1 = 9 .  

Now, let us continue with the second term that is in parentheses:

   " (2*10 +3 ) " ;

    →   2*10 + 3 = ?? ;

    →  Note the order of operations rules—{as stated above]; state that "multiplication/division" come before "addition/subtraction" ;

    → So:  " 2*10 + 3 =  (2*10) + 3 = 20 + 3 = 23 .

On "the right-hand side" of the given equation; we have:

        →  " 5 * (10 - 1) * (2*10 + 3) ;        

Replace the terms:  "(10 - 1)" with:  "9" ;

                                  "(2*10 + 3)" with:  "23" ;

And rewrite:

        →  F(10) = 5 * 9 * 23 ;

                     =  45 * 23 ;

                     =  1035 .

The answer is:  1035 .

Hope this is helpful to you.

        Best wishes!

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