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blagie [28]
3 years ago
7

Factor the expression 77x + 21

Mathematics
1 answer:
klemol [59]3 years ago
8 0
Answer:   7(11x + 3)  .
______________________________________________________
Explanation:
______________________________________________________
We are asked to:  "Factor the expression:  77x + 21 ." 
______________________________________________________
Upon examination of <u>both</u>:  "<u><em>77x</em></u>"  and "<u><em>21</em></u>" ;  we can see that "<u><em>7</em></u>" is the greatest common factor (GCF) of BOTH.   We can examine this visually, but let us write this out:
_______________________________________________________
21: 1, 3, <em><u>7</u></em>, 21

77x ;
or simply: 77:  1, <u><em>7</em></u>, 11, 77 
_____________________________
So, to proceed:
_____________________________
Write down a:  "7" ;
_______________________________
7 *( ????)
________________________________
Note the distributive property of multiplication:
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a(b+c) = ab + ac ;  AND:

a(b - c) = ab - ac ; 
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So , we write down a "7" ;
____________________________________________________
7*( ??? 
____________________________________________________
The first value is:  "+77x" ;  so,  " 7 * ? = 77x ?" ;

We can examine this visually and realize that the value is "11x"; 

or we can divide, as follows:  (77x/ 7 = 11x ).
___________________________________________
So we have already written down: 7* (??? )
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We can down rewrite as:  " 7 * (11x ......)
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 (since  " 7 * 11x = 77x ") ;
_____________________________________
The next (and in our case, final !) value in our expression is: 
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         " +21 " ; 
__________________________________________________
We have written down: 7* (11x ......)
__________________________________________________
So now, we need to determine: "7 * ? = 21" ?
__________________________________________________
We can inspect visually and determine the value is: "3" ; 
__________________________________________________
Or we can solve by division, as follows:
__________________________________________________
  "7 * ? = 21 ?" ;   21 / 7 = ? ;   21 / 7 = 3 .   The value is: "3" .
__________________________________________________
So , we have: " 7 * (11x .....) " ;   now we can rewrite as: 
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      " 7*(11x + 3)"  ;  or, simply:  " 7(11x +3)" ;  The multiplication is implied).
_________________________________________________________
   The answer is:   7(11x +3) . 
_______________________________________
Does our answer make sense?  Let us check!

The answer; " 7(11x +3) " is the factored expression of:  "(77x + 21)" ;
__________________________________________________
So: " 7(11x +3) " should EQUAL  "77x +21 " .  Is this true??
___________________________________________________________

Remember the distributive property of multiplication:
________________________________________________________
  a(b+c) = ab +ac ;
________________________________________________________
So;  " 7(11x +3) "  =  (7*11x) + (7*3) ; which equals:
_______________________________________________
  77x + 21 .   Yes!
________________________________________________________
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