Question

Factor the expression 77x + 21

Answer 1

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