Respuesta :
Answer: 7(11x + 3) .
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Explanation:
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We are asked to: "Factor the expression: 77x + 21 ."
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Upon examination of both: "77x" and "21" ; we can see that "7" is the greatest common factor (GCF) of BOTH. We can examine this visually, but let us write this out:
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21: 1, 3, 7, 21
77x ;
or simply: 77: 1, 7, 11, 77
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So, to proceed:
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Write down a: "7" ;
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7 *( ????)
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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" ;
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7*( ???
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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 ).
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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 ") ;
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The next (and in our case, final !) value in our expression is:
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" +21 " ;
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We have written down: 7* (11x ......)
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So now, we need to determine: "7 * ? = 21" ?
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We can inspect visually and determine the value is: "3" ;
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Or we can solve by division, as follows:
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"7 * ? = 21 ?" ; 21 / 7 = ? ; 21 / 7 = 3 . The value is: "3" .
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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).
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The answer is: 7(11x +3) .
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Does our answer make sense? Let us check!
The answer; " 7(11x +3) " is the factored expression of: "(77x + 21)" ;
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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!
________________________________________________________
______________________________________________________
Explanation:
______________________________________________________
We are asked to: "Factor the expression: 77x + 21 ."
______________________________________________________
Upon examination of both: "77x" and "21" ; we can see that "7" is the greatest common factor (GCF) of BOTH. We can examine this visually, but let us write this out:
_______________________________________________________
21: 1, 3, 7, 21
77x ;
or simply: 77: 1, 7, 11, 77
_____________________________
So, to proceed:
_____________________________
Write down a: "7" ;
_______________________________
7 *( ????)
________________________________
Note the distributive property of multiplication:
______________________________________
a(b+c) = ab + ac ; AND:
a(b - c) = ab - ac ;
____________________________________________________
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* (??? )
________________________________________
We can down rewrite as: " 7 * (11x ......)
________________________________________
(since " 7 * 11x = 77x ") ;
_____________________________________
The next (and in our case, final !) value in our expression is:
__________________________________________________
" +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:
____________________________________________________________
" 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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